Sort of, but keep in mind that San Diego is a completely different kind of zoo then the ones you've mentioned. All the old European zoos have dozens of heritage listed buildings, whereas San Diego's only major animal building is the reptile house. Some of the European zoos are over 200 years old while San Diego is around 100 (and very little of the original zoo is still around. San Diego has steep canyons, waterfalls and a jungle-like atmosphere, while the older European zoos are focused more on architecture (which isn't a bad thing!).
So in summary; San Diego has a lot of character, it's just different than the kinds you will find in Europe or even more Northern U.S zoos.