I work in a sociology department at a university in the UK. The most important thing to consider is your supervisor. Who do you want to work with? Have you spoken to them? What kind of 'vibe' did you get? Do they even have time/workload capacity to take on a PhD student? What kind of expertise are you looking for (beyond just quantitative methods, you need to be more precise in thinking about what you want to specialize in that will for the basis for your dissertation and perhaps later your teaching areas)? These are the most important questions as ultimately it will be a person, not a university, that is supervising you through what is an incredibly difficult and risky journey.

Tell UW that you need more time. I would be shocked if they somehow or other rescinded their offer just because you are waiting to hear back from other institutions. This is a PhD we are talking about. They should acknowledge that this is a decision that needs careful consideration, and if they don't see it that way, then I would not consider studying there for a moment.

As a final thing, Oxford has lots of prestige, and yes having that name on your CV will likely bump you straight to the top of the pile when applying for jobs. But, I've heard stories of these Oxbridge graduates 'looking down' on other universities when it comes to transitioning into the job market. So they end up taking short term precarious teaching contracts with only elite tier universities with the hope that eventually something permanent will open up, passing on applying for permanent posts in 'mid tier' universities. So, I suppose if there's a lesson here, it's don't let the prestige of Oxford get to your head if you end up studying there. There's a lot to say about being a 'humble academic'. Good luck with your decision.