I've been to both several times so here is my 2 cents...
Zoo- free parking, lots of different types of animals, hilly so you will get a stroller workout, closer to the ocean so more even temperatures, looks like natural enclosures, but with limited space, one of the best zoos we've seen. The tram there isn't worth it since you don't really see the animals well. Seems rushed.
Animal Park- charges for parking, hilly also so you will get a workout, more spread out so lots of walking, is inland so weather is more extreme, has a small water splash area for kids, cool playground for kids and lots of fake creatures to climb on, very pretty caroseul for I think $2, loads of animals with lots of space, beautiful to see, not a lot of shade for most of it, tram ride is very worth it! It is one of my favorites also.
Jenn