I have been to Wildlife World in about a year ago, and Featherdale about a year before that. Taronga goes back to school days so probably 20 years ago.

My recollections:

Taronga - good full day out but you could only see not be amongst the animals (may have changed now). Largest range of animals to see, both Australian and other.

Wildlife World - good compact way to see the major Australian animals, but generally in smaller housing and behind glass. A few hours will do it. You could pay extra to have a photo with a Koala (not really pet it) and I can't recall (thought it was a rip off) but seem to think it may be they take the photo and you need to pay to buy it.....not 100% on that though.

Featherdale - out in the suburbs of Sydney so not so convenient, but I think some tours combine with trips to the Blue Mountains. Basically only Australian animals, much smaller than Taronga and without the city/harbour views, but you get to walk amongst many of them and pet/feed them. The setup allows the animals to go to an animal only area if they are afraid. They had a few koalas set up with handlers which you could go and pet and take your own photos. I was very impressed by this and am not sure if it was luck being there at the right time, or it occurs all day.

Based on my experiences, if you want to be able to pet kangaroos, wallabies, koalas, and get your own photos with them, I'd go to Featherdale. If time is an issue and you are more interested in seeing the animals than touching them, I'd go to Taronga if at least half a day, or wildlife world if only an hour or two.

When I have out of town visitors, if they want to see australian animals, I take them to Featherdale.