As the Wildlife Centre is right in the middle of the city, environments for the animals are limited and manufactured. The Centre is in a giant shed, and there's limited 'outdoor' space. Compared that to the Zoo, where there's a bit more outdoor space for the animals to roam around.

For what you can see, I consider the Zoo to provide better value than the Wildlife Centre, all things considered. You can spend a whole day at the zoo, whereas, the Wildlife Centre can be done in a couple of hours, if that.

With regards to getting close to the Koalas, I think you'd find it'll be an extra activity costing extra pretty much anywhere. Also note that, 'getting close' to the koalas normally mean you can to get to have a photo taken standing next to one. You may be able to pat one, but holding one is a different story. Not many places allow you to do that for love or money. I believe there is a thread here about this a while ago. I read somewhere that it's due to the hygiene factors from humans to the koalas or something like that.

As to why the Zoo is the best, the Zoo is a zoo. The Wildlife Centre is a tourist attraction, and what I'd call, a 'wannabe' zoo. As I said above, being in the middle of the city, there's only so much space available. The Wildlife Centre focuses on species that are 'unique' to Australia, whereas the Zoo has more than just those. The Wildlife Centre tends to have a lot of insects, reptiles, snakes and desert-based animals.

The Zoo recently has an elephant born here. Apparently, it's very rare for an elephant to give birth in capivity.

The Zoo has also one of the best views of the city. It makes a great day trip.