Yup, if tigers and lions are what you want to see, then Cairns Wildlife Safari would be the place to visit.
I know this is a fairly old thread/post and you may have found out this already but I actually asked the tour guide (who is also the owner of Wait-a-while tours) about this and apparently he is the third owner and he bought the company a few years ago. I was wondering if nanoboy had the same guy as I did or if he had someone else - do you remember if your tour guide was a guy named Paul who was originally English?