I guess in the end Im really the most qualified here to help you with you quandry. However that does not mean I have the answer for you, Im just going to let you in on my situation.
I was in a very similar situation to you and it came down to some very personal reasons that I found myself at UOW. Haven't looked back since. I will be 21 when I graduate with an LLB and practical diploma, was offered a clerkship from 2 firms for this summer (didn't even apply) and have made many valuable connections with those in the game for when I graduate.
However my dream has never been to make it in the big leagues....I can't think of anything worse. I want to get in there and work with the little guys, not with the big firms. All signs so far are pointing towards me being a very happy camper when I graduate.
But I cannot pretend to know whether prestige matters when going for that big top-tier position NO ONE ON THIS BOARD CAN. I really wish everyone would quit pretending that they know because they don't. And they won't know until they actually do begin to apply for these positions.
Id like to be able to say with authority that prestige does or doesn't matter. But I can't. No one here can.
Yes, USyd has more prestige in the name than UOW. You will get that with a 150 year old university. Thankyou for stating the obvious guys, that was never a matter of contention. No one at UOW thinks they are at a more prestigious institution than students at USyd. But that doesn't automatically put every USyd student on top of every UOW student, Im afraid it just doesn't work like that.
Quit saying UOW is shit because its not. Its young, its growing. USyd is old, its established. There is no way of logical comparison between the two. I know for a fact that we have respected, ridiculously highly paid, authoritative teachers, the uni in itself is loaded (one of the only ones in NSW without money woes), and we have great electives and great facilities. Stop assuming you can judge it because its in Wollongong. Wollongong is a hole, yes, but the uni isn't. It is going from strength to strength.
Back to the OP, in the end if comes down to money I guess. Sydney Law School is a dream that many don't get the chance to realise, but you do. However, moving out of home is quite costly (hell, just plain living when you're a uni student is costly!) and you may find yourself working more than going to uni. But thats something I guess you need to balance. If USyd is a dream for you, go for it. But do it for reasons other than some of the lame ones put forth by the 'UOW is shit' brigade.