I cant say which is better cuz I've only been to the SF zoo. Its been kind of redesigned recently and it's good. It's right next to the ocean, which is bonus activity but can be chilly if the fog is in. My favorite thing is the big cat house where they feed the lions and tigers and you can get a good, close look at them!
I like the SF Zoo a lot -- especially the "Savannah," where different animals are all together in the same space. I never knew that Oakland had a zoo, but I only lived in the Bay Area for 5 years.
I haven't seen this at other zoos, but I like that they tell you when the different animals eat. Seeing a tiger a mealtime was definitely memorable. They're in a cage when they eat, and you can be up close (Eeeek!) but normally they're in a more open area and you are further away.
ETA: I also like that it's next to the ocean and you can get there on MUNI and walk back through Golden Gate park and see the Bison and the DeYoung if you want.