US PhDs are more competitive on both sides of the Atlantic (at least in US history), and certainly more competitive in the US. Especially when your US PhD options are Penn or Princeton. Doing coursework and comprehensive exams will prepare you to teach, which is what most professorships emphasize. The US degree will serve you better by setting you up for a broader range of options. While non-academics can be impressed by European institutions on your CV, in my experience most historians recognize a US degree as a better indicator of depth and breadth of training. And it's other historians who will be evaluating you for a job, if you want to enter academia. It's still possible for you to give yourself that depth and breadth on your own, and to be an impressive historian, coming out of a UK institution. But in the early going, you will have to work harder to demonstrate that you can teach, know your field well, etc., and I don't see a great reason to put yourself through that if you don't have to.
The only caveats: if your archives are all in Europe, yes, there's an advantage to basing yourself in the UK--when it comes time to research. In my mind this is still a secondary concern to having coursework, comps, and a longer, more competitive program in the US, especially if your US program options have some guaranteed fellowship years (no teaching) where you can base yourself in the UK for a research year or two. I'd imagine Princeton, at least, is good at this. If your 100% perfect advisor is in the UK, and your American advising options don't feel quite right, that's another reason to consider a UK degree over an American one, as advisor fit is the most important factor when deciding between reasonably funded offers. And, of course, if you have personal reasons for wanting to be in the UK, you're in the best position to make that judgment call. But if your goal is a tenure track job in a history department, my money is on the US degree as the easiest, most competitive way forward. There are great postdoc opportunities in the UK and Europe, which would likely be the most beneficial way to get some time in the UK into your career.
(all with a caveat that I don't know the History of Science job market) (and that getting a terminal MA in the UK can be a great option for boosting an application--my comments pertain only to a US vs. UK PhD dilemma)