1 Aircraft, more variety in America, prices a little less, but no where near as much as they were, training fleets on the whole in better condition,
2 Training, not that much between the two - some good, some bad as always, although the American approach to IRs is WAY better,
3 Different, but then the UK is different from France is different from many other European countries BUT the airspace in American operates in a more intuitive and seamless way,
4 FAA, CAA, EASA - the FAA are very good, the CAA are equally good, EASA (about to take over from the CAA) havent a clue and will cause much damage to GA this side of the Pond unless someone sorts them out soon,
5 Security - not a lot of difference, the security at large airports is I guess very similiar the world over (or at least that is the theory) and the security at grass strips - well no existant - it is the same here and the same your side of the Pond in my experience at least,
6 In France they love GA, everyone comes out to enjoy watching the aircraft, in the UK I think there is pretty good acceptance spolied by a small group who cant understand that having purchased a house next to an airfield that there are aircraft. Strange bunch.
I prefer the USA. In Europe everything stops at 18-00 (if you are lucky) and doesnt start until at least 0800 (if you are very lucky). We are obsessed even more than you with Health and Safety and with providing as second rate service as we can. We live in or close to a big continent (almost as big as yours) but contrive to make the seamless integration of air transport as difficult as we can. Dont believe we lot are a federal state of Europe the divisions in Europe are about as big as they have ever been.
On the flip side we speak proper English on the radio, still know how to keep a stiff upper lip, and are not adverse to the odd Tally Ho or an occasional silk scarf old boy.