THe main difference is that with the Safari Park, is that instead of seeing the animals up close and in an exhibit, there are 5 main field exhibits which are mixed species (you will see antelope, rhinos, giraffes, etc.) where the animals roam the whole area. It also focuses on mostly African Animals, where as most Zoo's focus on animals from around the world. There are some exhibits that are awesome, like Lion Camp, and that they have a Cheetah Run, which is a cheetah running after a lure. The Safari Park also has baby African Elephants that you can see. The Park is 1800 acres, but only about 800 has been developed into the Park, so you will need to do a lot of walking to see everything. Also, depending on the time of year you are going, it gets blazing hot up there, so that may be a consideration.
For the Zoo, the park is smaller, about 100 acres. It has animals from around the world, like most Zoos. It does have the pandas (one of four in the US) One thing to consider here is that the Zoo is having some major construction projects going on until Summer, and one of our larger projects will last until Spring 2013.
I like the Zoo and the Safari Park, and think that with the ages of your children they would enjoy either Park. My suggestion would be to sit down with them, and look at the website to see what is offered at both parks, and decide as a family. There website is
www.sandiegozoo.org. It has tons of information for both parks, and also the hours for the different times of the year, so you can plan things for when you will be there.