Usyd has got a diverse student population, so if you want to hang out with snobs, as with any university, you can. If you don't then there are more than enough non-snobby ppl to spend time with! The difference between uni and school is that there isnt the same pressure to spend time with a certain group of people, even if you don't like them, so snobbiness hasn't really a factor, in my experience. I was also a little worried about that before i got to uni, but it hasnt occured to me since i've been there that anyone has been snobby!
I was teased by some of my friends that i was going to the "snobby private school uni" before uni started, and although yes, there are quite a few of private/selective school people, i've found everyone to be heaps friendly. There isnt really much opportunity in the fleeting moments between lectures etc for anyone to be anything but that to you. It's only close friends that you would really see for extended periods of time, and if you don't like anyone, you don't have to see them. Simple!
I don't know about UTS so i cant comment really. Its hard to make generalisations about "people" at any uni. You should be able make a good group of friends wherever you go