Regarding 5e fighter vs. other 5e classes:
Fighting styles are only found on 3 classes in 5e. They are not accessed via feats, so they've become part of the niche of those classes. The fact that you could get similar effects in 3.5 on any class has no bearing on the 5e fighter's performance in the system it was designed for. The fighter shares fighting styles with the paladin and ranger, but only the fighter has access to all officially published fighting styles, and only the fighter gets them at level 1.
Action Surge is the only way in 5e to get an extra action with no conditional modifiers attached to what it can do. It's not just more attacks, though that's a powerful use of the ability, especially at level 11+. There's no other way to cast 2 spells from spell slots in the same turn in 5e because the bonus action spell rules of 5e prevent casting a regular action spell that's not a cantrip on the same turn. Haste limits the extra action to a single attack, Dash, or Dodge.
It doesn't matter how many ways a character could get lots of attack in 3.5. The only way you get more than 2 attacks on an action unconditionally in 5e is to be a fighter. The system includes various other ways to get bonus action attacks, and the fighter has access to many of those too. The ranger comes close but has to meet certain conditions to do so. Action Surge and the fighter's version of Extra Attack contribute to a big part of the 5e fighter's identity being, "does more per turn than other classes."
It seems like you're valuing these things based on how they're exclusive to the fighter in 5e, not due to their comparative benefit or objective power. If the claim were that the fighter specifically were much more powerful relative to the other classes then his exclusive access to those abilities would be very meaningful, but given that the claim is that the 5e fighter is much more powerful "relative to the system" than the 3e fighter, it doesn't matter that the 5e fighter is one of only a handful of classes that can get some fighting style bonuses and extra actions and attacks, only whether he gets those things when the 3e fighter does not, and he doesn't. Heck, even if Fighting Style were exclusive to the 5e fighter and Point Blank Shot, Power Attack, etc. were all exclusive to the 3e fighter, you're still talking basically the same effect, not an improvement.
Action Surge allowing multiple spells is certainly a huge boost that the 3e fighter doesn't have, but that only benefits the Eldritch Knight fighter, and once again is just a slightly different take on the 3e version; using the Eldritch Knight == duskblade comparison, the Duskblade gets the same free Quicken a few times a day, and using the Eldritch Knight == fighter/wizard/eldritch knight comparison the latter has lots of swift action spells and ways to get extra oomph from his spells (whether explicitly casting more per round with Quicken, extra actions, etc. or duplicating benefits with Twin/Chain/etc. metamagic and the like).
It has no role protection whatsoever. Even for the 2 level dip for feats, it's surpassed by the Psychic Warrior.
The 5e fighter has a lot of role protection. It has niches it is the best at within its own system. It needs no magic items to succeed and doesn't fail at its job when the party wizard decides to cast fireballs instead of buff and save-or-suck spells. A comparison of the 5e fighter's features to several 3.5 classes and prestige classes fails to encapsulate why the 5e fighter is still better built for the system it's used in.
Again, role protection is beside the point. If the question is "Do 5e classes generally give you more out of the box without multiclassing?" the answer is yes, but that isn't the same as "Are 5e classes more powerful across the board?" While "fighter X/barbarian Y/PrC Z" is less elegant-looking than "fighter [X+Y+Z]," it doesn't matter that everything in the latter comes out-of-the-box if the former has stuff that isn't in that box.
Regarding system math:
The rerolls are more statistically significant too. The 5e fighter has ASIs at level 6 and 14 that no other class gets. That's 2 more chances to take feats than any other class save rogue in a system where every other class only gets 4 chances to take a feat, and those chances compete with raising ability scores in a system that does not provide spells or any assumed WBL to compensate. The 5e fighter is going to have more chances to take feats, allowing room for a defensive feat like Resilient in a build optimized for offense. A CR 24 red dragon in 5e has a DC 21 Frightening Presence. In point buy, a fighter can reasonably be expect to have +1 Wisdom, meaning the fighter with Resilient could be expected to have +6 or +7 to Wisdom saves when fighting a CR 24 red dragon at an appropriate level. 25% to 30% chance to pass a CR 24 red dragon's Frightful Presence is a lot more of a chance than I'd give a 3.5 fighter to make against a 3.5 CR 24 red dragon's DC 35 Frightful Presence using only the fighter's base features.
This is a very valid point, and getting fighters back to their AD&D status of having high all-around saves is definitely one of 5e's best aspects. The above example is one where the "No items, no buffs, Final Destination" scenario breaks down, though. It's reasonable to be concerned with a lack of WBL for a low-level fighter or even a mid-level fighter due to a stingy DM, when having or not having a magic weapon is a big deal and DMs who love running "low magic (which means you get no gear, haha)" campaigns abound. But when you're talking playing in epic levels (when that requires an explicit decision to use epic material and weeds out the low-magic DMs many levels before), extreme wealth limitations like that go out the window. Even if a DM ignores the rules in order to deny a 24th-level fighter full use of all of his 1.8 million
gp, items granting mind blank
are on the order of 1/20th to 1/15th of his total wealth and are an obvious choice at those levels.
(And on the general PCs-vs.-system point, to get away from the fighter for a moment, spells like mind blank
are a good example of 5e characters being relatively weaker. When mind blank
goes from "immunity to anything mind-effecting" to "immunity to mind-reading and charm," the whole party is more vulnerable. I think that that limitation is a good thing, and usually houserule blanket-immunity spells in my games to make them more fair, but it's undeniable a step down in power.)
The naked, equipment-less 3.5 Fighter gets so screwed over by the system it plays in that it doesn't really matter what features you can build up to. It cannot reach adequate numbers to do its job without magic items and/or buffs from better classes.
The naked, equipment-less fighter is also mostly a strawman; both the 3e and the 5e fighter are expected to start with multiple weapons, a respectable suit of armor and/or shield, and adventuring gear, and despite the common concern about Big Six items in 3e a fighter doesn't actually need oodles of magic to do his main job (setting aside deliberately-under-CRed monsters like dragons), only really needing that when high-level adventuring starts happening in places where you need magic just to survive--and in those circumstances every other class needs the same magical support. I granted that point for the scenario because I was talking about what kinds of things the respective fighters can do, not what numbers the fighters have, but when talking about the latter taking equipment into consideration absolutely makes sense because "the system" in question takes it into account when determining base math.
Many defenders of the 3e monk use "But what if you're captured, stripped naked, and thrown in a cell?" as an argument for why the monk doesn't suck, and the response is generally that not having your expected gear is (A) a highly unusual circumstance and (B) against the wealth rules. Is it ideal that a fighter needs to use equipment or a party member for the above defenses or utility stuff? Not really; again, I'm not defending either the "3e fighter is subpar without his gear" or "3e dragons are way over-HDed for their CR" paradigms as good choices. But still, when comparing 3e fighter vs. 3e system and 5e fighter vs. 5e system, ignoring 3e wealth entirely is like ignoring a 5e wizard's spells because a DM could technically disallow the wizard from choosing any new spells despite this being contrary to the rules.
Also, critical hits do not require confirmation rolls in 5e, and no printed monster is immune to the extra damage of critical hits.
This is definitely an across-the-board boost, score one for 5e PCs, but like I said, 3e PCs get a lot more benefit from crits between higher base threat ranges, higher critical multipliers, and critical-triggered abilities. Plus, 5e crits only multiply weapon dice (which does include extra dice beyond weapon damage, unlike 3e), so while the rogue really really loves the new crit rules (though still loses out comparatively, since he can only trigger it once per turn), the fighter is probably doing about the same or less damage, rolling *[weapon dice + superiority die] + [Str (max +5) + miscellaneous damage bonus (max ~+5)] compared to the 3e fighter's [2 to 4]*[weapon dice + Str (max +lots) + miscellaneous damage bonus (max +lots)].
The Battle Master's comparison to Warblade is not as direct as you want to make it out to be. A Battle Master fighter uses most of his maneuvers after he has successfully hit with an attack. A Battle Master uses his maneuvers as part of his attack(s), not in place of a full attack action. The Battle Master could decided to Action Surge and use up all his maneuvers in one turn if he really wants to hurt and debuff something badly. He can use most of his maneuvers on opportunity attacks.
While the Battle Master maps most closely to a Warblade, only a few of his maneuvers are actually effects you need a warblade's maneuvers to duplicate. Disarming Strike maps to Disarming Strike, but you can still do a normal disarm attempt with any attack in either system (and doing so is equally suboptimal in either system if facing lots of natural-weapon-using monsters); yes, the 3e fighter requiring Improved Disarm is annoying and once again a point in 5e's favor, but the effect is available. Goad, Improved Trip, Improved Feint, and the like are all feats, all constantly available, and all usable off-turn. Parry and Riposte map to counters (usable off-turn), and Commander's Strike is only usable on your turn. Menacing Attack is the famous Zhentarim Fighter ACF and Maneuvering Attack is Order Forged From Chaos, and while the 3e versions are on-turn only, they can respectively affect multiple enemies (with Never Outnumbered) and allies (by default) at once, so there are benefits and drawbacks to each version. Rally grants temp HP where Devoted Spirit maneuvers heal, so that's another tradeoff.
For all the complex things 3.5 maneuvers could do, the Battle Master can trump their utility with one maneuver. A Battle Master with no more equipment than a non-magical bow and non-magical arrows can still knock a flying creature out of the sky.
Yes, the one area where the 5e fighter shines comparatively is the fact that his maneuvers are usable with ranged weapons where ToB maneuvers are restricted to melee weapons; trip-with-a-bow is actually something the 3e fighter can't duplicate, needing bolas, Bloodstorm Blade, or similar to do so. A single amazing trick does not a much more powerful class make, though.
The 5e Eldritch Knight is a not a Duskblade if you take any more than a cursory glance.
Like I said, a fighter/wizard/eldritch knight also maps well to it and blows both the duskblade and Eldritch Knight fighter out of the water. But really, an Evocation-focused spell list, the ability to cast+attack in the same round, and short-range teleportation make them both similar kinds of gish. And again, 3e has several attack-and-cast-at-the-same-time and teleport-and-then-attack abilities, and while it's convenient that a new player can just pick up the Eldritch Knight instead of building something more complex, that speaks to ease of use, not power.
The 3.5 troll is more damaging with a full round attack due to a higher attack bonus, a higher Strength score, and its Rend ability.[...]The 5e fighter at that level makes 2 attacks at the same bonus regardless of how much he moved during the turn, but the 3.5 fighter makes its second attack at a penalty and only if he stood still.[...]The 5e troll has numerically more hit points, but it's going to be subjected to more damage (3.5 optimization not-withstanding).
Rend doesn't actually give it appreciably more damage on average, since the 5e troll has higher base claw damage and Rend only triggers if both claws hit. The 3e claw/claw/bite/rend is 1d6+6/1d6+6/1d6+3/2d6+9, while 5e claw/claw/bite is 2d6+4/2d6+4/1d6+4, for a total of 5d6+24 vs. 5d6+12 with Rend and 3d6+15 vs. 5d6+24 without; 3e works out higher on average if both claws hit at least 75% of the time, and given a 3e fighter's higher AC (at least higher enough to account for the 3e troll's extra +2 attack) that isn't at all guaranteed. The fighter, meanwhile, will hit a troll more often (3e's around +11/+6 [BAB +5, Str +4 or +5, +1 or +2 from a magic weapon, Weapon Focus, etc.] vs. AC 16, compared to 5e's around +7/+7 [+3 proficiency, Str +2 or +3, +1 or +2 miscellaneous] vs. AC 15 for both attacks), so even accounting for spike damage from Action Surge (and ignoring optimization, which favors 5e since the 3e fighter gets a lot more out of that than the 5e fighter does) the 3e troll is likely taking more damage. And while a fighter loses out on a bunch of damage if he moves more than a 5-foot step, so does the troll, so it's a wash.
The 5e troll has more hit points and higher regeneration. The troll's regeneration is relatively weaker in 5e because access to on-demand fire and/or acid damage is easily achieved by someone in the party. Furthermore, regeneration isn't the same mechanic across editions. 5e does not have non-lethal damage as a separately tracked number that regeneration applies to. The 5e fighter is still attacking the same HP pool with his weapon as someone else is with acid or fire, and 5e's regeneration stops functioning for a round if the troll takes a point of fire or acid damage. 5e regeneration 10 is not stronger than 3.5 regeneration 5 just because it's a bigger number.
The difference between the two forms of regeneration is largely immaterial unless you're only poking the troll for 1 or 2 regeneration-bypassing damage in both cases, since "take 5 damage that you don't heal" and "take damage, don't heal 10 this round" amounts to the same thing if you're dealing at least that much fire or acid damage with each attack. It does matter if you're fighting lots of monsters at once, since whether you need to poke it one more time and it's dead or you need to either keep poking it for a bit or take a full-round action to CdG it matters during a fight, but at the levels when the troll is the most dangerous you'll only face one or two at once, and post-combat cleanup is pretty simple in that case.