If you want to progress to US I would do it at LSE (MPhil could also take you to the States but I think LSE has more tradition in doing so). If you want to stay in Oxford, I would do MPhil. I speak from the EME LSE perspective. I have talked to a lot of people that have done EME and they have recommended me to stay a 2nd as a RA at LSE to get better letters. I know different cases but research experience after it is more the rule than the exception. Plus, I do not know the rankings of all people I have talked to (except one and was the best) but I think that distinction takes you to the States. I think MSc is not that further away from EME (MSc more economics inclined whereas EME more mathematically inclined). I think MSc is well regarded in the US. Personally, I am going to accept EME over other PhD offers and take the real analysis course (cheaper for LSE students) in the summer between the master and RA, so if you finally accept LSE as well we can be in contact! This is what I think, but suggestions from others would be better