The training for the two is some 95% common. With a slight extra (the FAA night X/C for example) you meet the extra requirements for the FAA PPL also, and you just do the FAA checkride at the end.
The other extras are an FAA medical (but there are doctors here who can do both medicals at the same time), the FAA written exam (1) which you can do here or (for far less) over there, and of course the pre-checkride oral exam.
Otherwise, to do an FAA PPL at a later date, here in Europe, you have to jump through a load of extra hoops and spend a big pile of money. I did that a few years ago and it cost me several thousand quid, hotel stays etc... Then, for a few years, it became impossible altogether (no checkrides). I was doing that because I was working towards the FAA IR. Had I done my JAA PPL in the USA, the extra cost of picking up an FAA PPL at the same time would have been at most 1/10 of what it cost me, and 1/100 of the hassle and aggro.
An FAA PPL is yours for life. Never expires. Nobody in Euro-land can take it away from you - ever.
Anywhere in the world, you can jump into a US reg aircraft and fly it, worldwide.
To exercise its privileges you need to renew the medical, and have a BFR. If your address changes, you get onto the FAA website and for $2 sort it out (unlike the FAA 61.75 piggyback PPL which has cost plenty of people hundreds, and endless runarounds, to sort out changes on over here, recently).