Be aware that the UK is currently planning to leave the European Union, where a lot of high quality funding for projects is coming from. The next few years are a little bit unclear in that regard.

You posted this clarification while I was writing my response.

Based on the additional information, I would suggest that a USA PhD research op would present more advantages.

Notwithstanding that, if you are attracted to the adventure of studying at Oxford and are able to secure a well-funded research position then it could be a fantastic experience.

My apologies, and thank you, your advice makes a lot of sense!