I have been to both places on multiple occasions. One is much easer to get through in one day than the other buts its still possible for both. Heres my personal route for when I go through the zoo.
It is possible to see at least 90% of the San Diego zoo in one day, especially since the new Children's zoo is still under construction. Definitely start with Africa Rocks (penguins, baboons, lemurs, meerkats, honey badger, etc) its the newest addition and right by the entrance. Along the way there you can walk through Australian Outback (koalas, wombats, Tasmanian devils, birds, etc) and the Urban Jungle (giraffes, cheetahs, rhinos, kangaroos, etc.) which are both pretty small areas. Afterwards head back up the hill through Asian passage and walk through The Lost Forest (primates, hippos, tigers, hundreds of birds etc.). This is essentially one giant exhibit with several sub exhibits inside it. You will likely spend most of your time here within this area and I warn you it can be a bit of a maze to navigate. You can grab lunch at either the Treetops Cafe by the gorillas or at Albert's by the bonobos. Both are very good dining options especially for zoo food. Once your out of The Lost Forest (I recommend exiting by the Ituri Forest area with the hippos and okapi at the top left of the area on the map) make your way to the Northern Frontier (polar bears, caribou, arctic fox). Then you can walk down Elephant Odyssey (elephants, lions, jaguars, capybara, condors, etc) and you be back near the entrance. Feel free to go back in The Lost Forest and cover whatever you missed the first place and come back out near where Panda Trek (without pandas it includes leopards, red pandas, takin and the rare mang mountain pit viper) is.
There is a Birds of Prey area along this same path. Again, I'm sorry if this all sounds a bit convoluted but frankly its a challenge to get through this place in one day. However, you will still have a really good time because this is a fantastic place.
The Safari Park is much easier to navigate. As soon you enter I recommend heading straight towards the boardwalk that will take you to three exhibits that are sort of separate from the rest of the park. The Tiger Trail, Condor Ridge and Australia Walkabout. Your going to want to check out the walkabout first as its home to the only platypus outside of Australia and the crowds can get pretty big from what I've heard. Then you can probably get through the rest of the park without any major issues. Its pretty much a straight shot towards the tram tour around the field exhibits and you really shouldn't have any major issues. I recommend lunch at Mombasa Lagoon, the food is really quite good and the seating overlooks a beautiful island for shoebill storks, pelicans and dozens of the ducks.
Sorry if this a bit hard to follow, but either way you will have a great time at both of these places. Have a good trip.