So, there is a cap for passive animals, shared among all loaded chunks. So, the immediate 16 or so chunks and about 12 surrounding the spawn point of your world. Since the spawn points are always loaded and you have dogs, it's very likely there are a lot trapped in your spawn chunks or that you have some kind of farm.
I'm not sure about 360 and obviously servers are variable depending on how many chunks are loaded by players, but for a PC single player world, the passive animals is around 80 per dimension, 80 each in the Nether, End, and Overworld.