A level 1 Fighter is just plain better than a basic wolf, the Druid's AC
Really. Permit me to express my polite disbelief in the form of a side-by-side comparison:
HD: 10+Con vs 2d8+4; a Fighter with 14 Con or less (quite common) is at a disadvantage, and only a Fighter with 18 Con or more has any advantage. Plus, some effects are HD-linked, and while most of those won't care about the difference between 1 and 2 HD, some do (e.g.
sleep's cap may be forced to leave out a character because the wolf takes up double capacity). Also, some DMs may permit PC-associated creatures like AnCs to use PC rules for starting HP, in which case the wolf jumps up to about 16 HP. Advantage: wolf, by a small margin.
Initiative: +Dex vs +2; probably about equal most of the time, although the Fighter can spend their feats on Imp Init. Advantage: Fighter, by a small margin.
Speed: 20/30 vs 50. Advantage: wolf.
AC: 15+size+Dex vs 17 if almost all Fighter starting money goes to armor and one-third of Druid starting cash goes to studded leather barding; 14+size+Dex or less normally. Most Fighters will not have 16 Dex, which is necessary for parity with a realistic budget, and may well have only 12 or even 10; not many will use shields, given the serious drop in offensive potential. Advantage: wolf.
BAB/Grapple: +1/+4 vs +1/+2. Advantage: Fighter, assuming grappling is a thing that's important.
Attack: greatsword +4 (2d6+4) vs bite +3 (1d6+1). Advantage: Fighter, definitely.
SA/SQ/feats: One bonus feat and one level feat vs trip, track, low-light vision, and scent; a Fighter desiring to trip needs to spend both those feats and will still lack scent (and tracking, but that's fairly minor, and usually also low-light vision, but that's a race choice away). Alternatively, they can spend those feats on other things, but tripping is usually pretty high up there. Advantage: wolf, possibly.
Saves: Fort +5/Ref +2/Will +0 vs Fort +5/Ref +5/Will+1; assuming 14 Dex, 14 Con, and 10 Wis for the Fighter. Advantage: wolf.
Abilities: If the wolf can rearrange these scores with an array, rolled scores, or point buy most of these entries become more favorable for it.
Skills: Usually 4 skill points and a terrible list vs 5 skill points and a terrible list with a racial bonus to something irrelevant. Sometimes the Fighter has 13 Int for CE, in which case this goes up to 6 vs 5. Advantage: ???
Origin: PC vs 24-hour cost-free ritual. Advantage: wolf.
Obviously, there's a fair amount of variability here, but it's hard to argue that the Fighter is "just plain better"; it's hard to argue the Fighter is better at all.