There are a few points you seem to be ignoring here that I feel compelled to bring up.
That's fine but prepared to have some returned.
First, beguilers can actually end encounters - charmed opponents won't fight back and don't need killing.
First, Charm/Dominate doesn't work against Constructs, Oozes, Plants, Undead or Vermin. Secondly Charm/Dominate
Person doesn't work against Aberrations, Animals, Dragons, Elementals, Feys, Giants, Magical Beasts, Monstrous Humanoids, or Outsiders. Thirdly, not all Humanoids know Common by default and Charm/Dominate are Language dependent. Fourthly,
they don't end Encounters.
Charming a creature to stop fighting while the Fighter is next to him grants the creature a massive +5 Bonus to his Save (currently being threaten), and you can't even convince the creature to allow you to pass without an additional
charisma based check, because it's against what a guard or patrol or hungry cannibal would normally do. And if you attempt to circle the guy to "ambush him" he auto-breaks Charm (any threats break it).
Dominate on the other hand awards additional Saves with a +2 Bonus
per order. If you Dominate a creature and tell it to stop fighting when it would normally fight, it resaves. Then you order it to show you the way, it resaves. And when the creature does Resave, he can instantly
start a new Encounter except the rest of your Party is Flat-Footed during his Surprise round. That's pretty f'ing harsh when you think about it.
Phantasmal Killer, the Mind-Affecting independent Cloudkill, the rape you Circle of Death, and lol Implosion
end the Encounter. Charm/Dominate just delays it, *if* they work in the first place.
They BOTH get the armored mage class feature, so I'm not sure where you're getting warmage higher AC from.
You didn't actually read the entries did you? Warmage gets Shields, Beguiler didn't. So while one of them is waiting until they can afford a Mitheral Buckler, the other is looking forward to increasing his already obtained Bonuses.
The beguiler gets dispel magic and greater dispel on its spell list as well, thus making slashing dispel an argument against the warmage. The warmage advanced learning specifically calls out wizard spells as learnable, so warmages cannot get desecrate and holy word because they are not wizard spells.
I did miss Dispel, good thing I didn't care too much about. Also "Wizard Spells" can be proven it's not synonymous with "Wizard Spell List" and when I mentioned Holy Word I was talking about Saveless Encounter Winners, sticking to generic Wizard Spells only does not remove Amber Sarcophagus's Save-less stasis or Iceberg's FoM bypassing auto burial & CL/d6 damage so the point still stands.
As far as blasting goes I still can't figure out why I'm expected to care about the warmage blasting superiority. Yes, you can do a small pile of damage if you dump a ton of character resources into it.
Damage by far is the easiest trait to optimize in D&D.
Lastly, there's no reason to play a warmage in the first quarter of the game.
I'm going to take this last standing point of your rebuttal as agreement that later on the Warmage is better if you don't mind. And it all comes back to how you build them.
For instance, a gish focused Warmage may tank his Edge (it's not that significant anyway) and focus on Strength. Fist of Stone is a 1st level Spell that not only grants a Natural Weapon allowing the Warmage to make multiple Attacks per round while the Fighter and Barbarian are five levels away from such, Fist of Stone
gives a +6 Enhancement Bonus to Strength. Holy crap right? A brute force Warmage makes a better Fighter than a ACFed to holy hell Barbarian.
Alternatively you can play as the blaster archetype you're supposed to. The Elder Giant Magic Feat can be taken now and retrained out later since you won't be using it with Creation/Fabricate. Precasting and holding the Charge to Shocking Touch means you have an opening 4d6+IntMod Touch Attack for at least three out of four Encounters per day. A Greatsword swinging 18 Str Meleer deals 13 damage so you're already dealing more than mundanes with a better hit chance (touch based). But say you want to take another step in, Iron Will and Reserves of Strength via Flaws brings this to 7d6+IntMod thanks to breaking die caps, now you're dealing Ubercharger damage as a Touch Attack for probably all four Encounters (and said ACF'ed to holy hell Barbarian has Frenzy for only a single Encounter).
Either way, the Warmage out 'DPSes' everyone else and later on he never even had to pay for those advantages.
Level 4 rolls around, the Beguiler gets his Glitterdust. Yeahee, he can has a Save-vs-Blind for 4 rounds, hits a 10ft area. Utility support of revealing hidden creatures (like a torch) or Invisible ones (like that Pixie because everything else auto-loses Invisibility when they attack). The Warmage also gets a Save-vs-Blind, Pyrotechnics. Nearly the same Duration (avg 3.5) but trades in needing a torch or candle to center on for to
duodectuplet the affected area (120ft vs 10ft). Additionally, you can choose to deny the Will Saves against Blind and use the Spell to create a 20ft cloud that negates vision and instead they Save against a -4 penalty to Str/Dex. Oh, and without Feats he deals 28+ damage per round now (Scorching Ray) which is more than an Ubercharger without Rage so you can already retrain those Feats out.
Level 6 rolls around and the Beguiler gets Save-vs-Slow and opponents have to choose between Attacking or Moving, awesome right? The Warmage has Gust of Wind to move things about and counter fog spells, Poison's Ability damage, Sleet Storm for superior-Grease, and Stinking Cloud's Slow-but-you-never-get-to-choose-to-attack (ie it's
better than Slow). He also had Shatter two levels ago which can be used to negate a Cleric's Spellcasting, a Ubercharger's damage, or well anything else you can think of.
So by "first quarter", I think you mean level one. And under the circumstances that the Warmage's one-hit kills is depreciated when you have one to two other party members capable of doing such as well.