Depends where you go.
I've flown around some lovely quiet areas of Arizona and California, or for that matter most of Florida, that make Popham on a Saturday look incredibly busy.
I've never, in the UK, seen anything as scarily busy as Long Beach CA on an average day. (Okay, maybe the PFA/LAA rally, but even that doesn't involve full ATC and slotting in with arriving airliners.)
But RT is different, how you obtain data about safety of a flight is different, and the places in the USA with large flight training industries tend to have much better - and certainly different - flying weather to most of Europe.
There is sense in learning in Europe. On the other hand, learning somewhere like CA or AZ, then coming back with an expected budget of half a dozen hours each groundschool and flying with a local instructor over here will tick the same boxes, but probably be much faster and a little cheaper.
I've never noticed any particularly different "magenta line" tendency in the USA compared to Europe - the culture is pretty similar in that regard.
G