If you hadn't been to the zoo before, I would definitely suggest the zoo over the Safari Park to first-timers. I actually work at the zoo, so I'm usually biased in that direction, but since you HAVE already been to the zoo, I think it's worth giving the Safari Park a try.
There are a few downsides you should prepare for -there is not as wide a variety of animals, and they are not as easily accessible. While some of the animals have exhibits that you can access through walking trails (be warned, some are STEEP!), many you only get to see on a tram ride, so if they are hiding, or far from the tram, that's the only opportunity you get in most cases to see them. The good thing is that since the Wild Animal Park became Safari Park, they made some changes. One of which is that now a general admission ticket includes UNLIMITED tram rides, whereas it used to only include one. That means if you don't see all the animals you wanted on the first, you can always give it another go (or two, or three, etc.) later in the day.
That park has two new baby cheetahs, a BRAND new baby elephant (two weeks old), and a new elephant exhibit, so if you're going soon, definitely keep an eye out for those little guys!