I try to roughly calculate the power of a class ability in terms of 'feat equivalents'. That is, "How many feats would you pay to gain this class ability?"
To cast 4 spells of your choice of every level 1st through 9th is worth at least 36 feats, plus another 2 feats or so for the ability to cast cantrips. In that light, a class like Wizard is getting the equivalent of multiple bonus feats each level, one for each spell slot that they gain. Obviously the later 'feats' in the 'chain' are more powerful than the earlier ones because they give more powerful spells, but this is assumed to be balanced with feats that likewise increase in power as you move down the chain. It's easy then to see why the 11 bonus feats a 3.X fighter gets are insufficient, as the Wizard's class abilities are equivalent to roughly 44 feats. Granted, the fighter gets some feat equivalents out of better HD (say 6 or so), better BAB (say another 4 feats worth), and better weapons and armor (worth about 3 feats), but it loses on skill points and skill selection (worth about a 1). So viewed side by side you might rate the stock 3.X fighter as worth about 24 feats, and the stock 3.X wizard as worth about 45 feats. Clearly the fighter needed better abilities at higher levels, something Pathfinder tried to address. Equally, it's easy to see why they are fairly equally useful at low levels (1st and 2nd) without a lot of modification.
I don't think you can ever get this down to the level of point buy, but you can get a rough approximation of where things are by asking how much would you pay for it.
Keep in mind that many powers are inherently situational. Even under this approximation, they build of equal power but greater utility in a wider number of situations is more powerful. That's why Wizards, Druids, or Clerics - particularly when they have access to wider spell lists - are usually considered superior to any other class (even without the design gaps). They have the ability to find answers for any problem they are faced with.
How powerful animal companion as an ability actually is depends on its replacement cost in your game. If for example, a character can use animal handling to train a smart animal with sufficient tricks, that the pet now acts as an effective companion, then the class ability is only marginally better than having 'handle animal' on your class skill list. The Leadership feat is widely regarded as the most powerful feat or ability in the game, bar none. But if your DM runs the game such that you can gain loyal allies through appropriate role-play, then having the Leadership feat is only marginally more useful than having Charisma.
In general, I would say that animal companion is a very powerful ability indeed. In my opinion, versions that cause your companion to 'level up' with you are almost too good, balanced only by the fact that there are things that are even more broken.