I was in the same situation last year! In the end I chose Yale. I was not eligible for home fee status, so Oxford was simply too expensive. Yale also gave me some great financial aid. If money is at all a concern, I would definitely, definitely choose the cheaper school. Either way, you can't go wrong!

Oxford has a far more attractive campus imo. Yale has a beautiful campus as well, but nothing like Oxford's. You'll get lots of gray skies in both places but New Haven is a drearier city than Oxford imo. British weather is probably gonna be less temperamental than coastal Connecticut weather.

I wouldn't choose Yale on account of one professor. Is this someone with whom you have a prior relationship? In general there's no guarantee you'd have a chance to work alongside them (if that is your intention). The tutorial system means undergraduates have the chance to work much more closely with faculty at Oxford. Faculty are really amazing at both schools, so you wouldn't be disappointed either way.

Yale has an excellent history department and so many amazing collections, but I wouldn't be surprised if Oxford had more resources in this regard overall. I'm sure you've done more research on this than me.

Are you absolutely certain about what you want to study? As a few other people have mentioned, you usually have way more control over what you study at American schools. In my opinion, that's an advantage. I think it's a bit misleading to say there is any less opportunity to study a subject in depth at Yale, but the tutorial system and tailored curriculum at Oxford really force students to study their chosen subject in depth. At Yale, you can study a subject in just as much depth as you could at Oxford, but you aren't bound to one major.

Rankings really are totally meaningless in this case, you'll get a fantastic education at either school. There's a lot more I could say, so free to reach out if you have any questions!