It totally depends on what you're in the mood for.
Both require LOTS of walking a lots of hills. The Safari Park (the new name for the Wild Animal Park) has a tram that you can ride throughout a lot of the park to rest your feet and the zoo has a bus tour that covers about 60% of the animals in the zoo, as well as an express bus that helps you get around the bus. Both the tram at the Safari Park and the buses at the zoo are included with regular admission.
The two parks are the same price. The zoo has free parking while the Safari Park charges $10 for cars (more for large trucks or RV's). The Safari Park is in Escondido and a little off the beaten path while the zoo is in San Diego proper. The Safari Park gets a lot hotter than the zoo in the dead of summer, so that's something to factor in.
They are both great, but offer different things. In the Safari Park, the focus is primarily on African animals and you ride a tram through large enclosures to see herds of animals "in the open". There are a lot of animals, but less variety than the zoo. The zoo is more like a traditional zoo and has tons of animals from all over the world. If you're looking for koalas, camels, kangaroos, polar bears (or any bears for that matter), leopards, otters, wolves etc., the only place to find those is the zoo.
I promise you'll have fun at either, it's just up to you what you think your family will enjoy more.