Both zoos are nice, but the Wildlife World Zoo is very expensive, especially since they put in the aquarium (I guess they need to pay for it!). The Wildlife World Zoo is pretty flat and easy to get around, the paths are dirt,and you can pretty much see all of the animals. They can't hide as much. It has a playground and a petting zoo.
The Phoenix Zoo has hills and large. They do have a zoo train that you can ride (extra) and get off and back on again. They have more animals than the Wildlife World Zoo, but sometimes they're hard to see, they have hiding places. In the summer there are water play areas for the kids. They have a Fisher Price play area that's new for kids 5 and under, a petting zoo, and a playground too. They do have the stingray and shark area where you can try to touch them (extra price). Their paths are mostly paved. The best time to see the animals is in the morning when they're awake and eating breakfast. You can usually see them rather than later when they're snoozing and hiding.
I have a membership for the Phoenix Zoo. You get a discount at the store, a few free passes, a few free train rides, discount on the train, discount to the stingray bay area.
I don't know about not bringing your own food into the Wildlife World Zoo. I've done it before, that may be a new thing or I didn't get caught :). They don't have "real" food there unless there is now with the new aquarium (I think there's a new restaurant). It's been awhile, because of cost, that I've been there. Their membership is very expensive. It was something like $100 per adult and $50 per kid. If you plan on going all the time, I guess it's worth it, but not to me.
The Phoenix Zoo's membership is alot less. I paid around $120 and that's me, a guest (or a named adult, I chose to use guest so my hubby or my mom or my dad could go and not just the person named), and 4 kids. It's farther away, but that's okay. We make use of it. They seem to have a better variety of food, but still not great, in my opinion. We usually bring a lunch. Adults are $16, kids 3-12 are $7, seniors are $11.
There are coupons in ValPak or the other coupon magazines for the Wildlife World Zoo for $3 off a ticket. They do have a price for the zoo and aquarium or just the aquarium. I think the adults are $26.50 and the $13.95 (9 a.m. to 6 p.m.) for the zoo (2 and under free), and the aquarium only (5 to 10 p.m.), the adults are $16.95 and the kids are $8.95 (2 and under free).
It's a bit of a long answer; I hope it helps. Both are good and I recommend both. It just depends on what you're looking for and how much price matters, I guess. Have fun!