In my opinion hunting is really only good very early on in the life of the fortress, for a couple of reasons:
First, it is actually possible to kill most/all of the creatures in your biome, so if you wantonly overhunt the landscape, you'll run out in a couple years. For a lot of the game animals, you're probably better off cage-trapping then taming and breeding them, if you want to keep that particular species in your dwarves' diet for any length of time. Second, for large animals (like for instance, Elephants which currently starve since they can't feed themselves fast enough,) or really dangerous ones that you don't want to domesticate, capturing them and killing them in a more controlled setting will increase survivability and convenience quite a bit. (I'm also of the opinion that using cage traps to capture wildlife isn't nearly as gamey as spamming 100 of them to capture entire sieges.)
Finally, once your farms/pastures are up and running, you've probably already got more food than you know what to do with, so having lone dwarves roaming outside your protective walls with sieges showing up all the time doesn't really serve a purpose. If a dwarf is good with a crossbow, there's plenty of goblins and elves. (Of course, if you want to hand your helmet-snake-bone-loving baron a crossbow and tell him there's a family of tasty giant badgers outside, then that's another matter entirely.)