Yeah, I did just that.
You can get an FAA SE & ME CPL/IR, CFI for about 28,000 dollars with first time passes on the minimum hours (quite realistic with excellent training--I managed it after signing up with a British flight school here). A little bit more cash for CFII and MEI which is a must for the serious wannabe, clock up 1,500 hours for free as an instructor, and then do the ME ATP flight test (only one written exam for that).
The money I saved by not going the JAR-FCL route I spent buying my own single-engine complex (a Mooney). Seemed like a good deal to me. Flexible hour building; no need to bring the plane back the next morning. And I can sell it if I run out of beer tokens.
So I'm living at the beach in San Diego, which is overrun with stunningly attractive girls wearing very little, and good bars, instructing during the day, and when it's quiet take my own plane for a spin for some skiing, or a few beers in Vegas, Phoenix, San Francisco, Portland, Seattle or Vancouver (yep, can get to Canada in a day). Life is good. I can thoroughly recommend it.
Be warned, though. JAA do not honour their obligation under ICAO to recognise other authorities newly minted professional licences and converting to JAR, practically and financially, is not an option. However, things are always changing with that lot (in the last year the JAA's 'conversion' requirements have changed at least 3 times, most recently last December).
No point considering the FAA route if you want to go back to the UK though, and definitely not worth considering if you haven't thoroughly researched US immigration requirements if you want to work there as acquiring a work visa is no easy task by any means, and can be a very long road.
Drop me an email if you want more information.