From what I have heard -around this site mostly- (not a keeper or volunteer myself), a major difference is that generally european zoos tend to use more often carcasses for feeding, while us zoos avoid it. Moreover, zoos in the states, even if they use carcass-feeding, avoid doing it during open hours.
There is also a difference when it comes to the use of euthanasia as a tool of population management. European zoos generally use it more that their american counterparts.
Lastly -and correct me if I'm wrong - but I seem to remember thet the Eaza recommends the mixing of grevy's zebra and discourages the mixing of mountain zebras, while the aza recommends the opposite.
However, it is important to note that even amongst Eaza, there are differences, since some zoos cannot implement euthanasia for population management due to local legislation. Also, as you may have noted, I used the word generally often, as it is hard to lump together the management styles of zoos from all around eaza or Aza.
