I have offers to both for PhD study, both with the supervisors I've wanted to work with. The biggest issue for me to make the choice right now between the UK, US, and another overseas university is all about money. You have to pay tuition (~ 19k pounds/year for overseas students) and some other fees as well. UK schools do make offers to a lot of students each year but only very few get scholarships, and it's these people who go -- generally speaking, one would feel a little uncomfortable being the only person in a department who isn't getting any funding because that could potentially negatively affect job prospects.
Re. other differences: less teaching requirements, little to no coursework, and much LESS politicised than the US universities.