Masters in US or (Masters + MPhil) in UK
In terms of PhD admission prospects, both the UK and US have top quality schools with international renown. However, if you're planning to study PhD in the US, having a masters in the same country can help in creating more relevant connections between other researchers, and therefore affecting your chances for PhD admission.

In terms of program structure, there are differences like you mentioned. However, even US institutions start off with a more course-heavy workload and gradually move on to a more research-focused program (second year). Also, getting familiar with basic research concepts and ideas early on (as with US programs) is not necessarily a bad thing and you shouldn't worry much because there are many cases like you who have come from a non-CS background. If you get accepted, the department is well-aware of your background and potential capabilities

EDIT: Empirically, UK institutions offer less funding options especially at the masters level. Even at the PhD level, most of the funding I've came across are offered as partial awards that don't cover the full tuition and living costs. It is still possible to obtain full funding at a UK institution, but overall, funding is usually an important factor in deciding your place of study