If you are only going to do one, do the zoo.
If your family is big animal lovers, do both! But be prepared for a lot of walking. The Wild Animal Park is huge and very hilly (actually, so is the zoo, but it's more manageable IMO).
The WAP has animals you won't see anywhere else - the most rare rhinoceros in the world, the second tallest giraffe in North America, and several baby animals that were just born this past fall - an elephant, giraffe, and some others.
But at the zoo you can see pandas, including a new baby that was just put in the exhibit a few weeks ago.
I would suggest looking at the website for both parks (sandiegozoo.org) and if your family has animal preferences, go from there.
The zoo has a great Children's Zoo, but the WAP also has a petting zoo and a really neat playground with an amazing view:
Have fun!