Hi Smokeydog,
Not sure if you've made a decision yet, but I just wanted to tell you that I was in the exact same boat recently. I had an offer from a top US school with incredible funding and offers from Oxbridge with the potential for funding. I'm also an international student, and I also would absolutely not have been able to attend without funding. I chose the US. And I am so very happy I did! Oxbridge was attractive because it would have been much shorter, but in terms of reputation and academic rigor, I don't know that Oxbridge's really any better than top US schools.
I've had a good experience of grad school and grad life, and I have to say, a big part of it is because of the funding (and location! -- weather and such), so I think those are big things to consider (along with what students in your potential programs say about the departments' cultures). So, I chose great guaranteed funding over the potential to get funding (which also translates to the potential to not get funding). I totally get what others here mean when they say you can accept the US offer without being legally bound or anything, and then bail on them if Oxbridge works out. I have to say though, that I think it'd be most unfortunate if you accepted a place knowing you might bail, and then bail, only because that means there will be someone out there who could have gotten that spot who won't, and especially given it's a funded spot at a top school, that'd just be most most unfortunate.
Good luck! and feel free to PM me if you want to talk more.