What Johns said is also true about the pests Animal Control hauls away from backyards in my big city (Houston).
Some animals are "relocatable" because they can fend for themselves in a new area. But certain other types are not acclimated to their new area (even if it's just a mile away), or are carriers of diseases, or simply "weaker" in some way, and therefor not suitable to just dump in a new area.
I forget which critters get moved, and which get gassed, but the Animal Control guy said most of them are just put to sleep. At least with the gator, the skin and meat can be used.