I'm biased, but I say go FAA then JAA. I like the idea of having both JAA and FAA papers. It depends on what you want to do in the end I guess. Also, I think that living abroad for a while can be beneficial to you (anyone) as a person, besides your flying skills.
I've done FAA first, then JAA conversion. I had a lot of hours when I got back, so the amount of hours I've flown for my conversion isn't really representative I think.
Do remember that under UK JAA rules, there is still a minimum number of hours of training required, even if you would not need it.
Work out the exact costs. Make sure you factor in cost of living/transport, etc. If you don't specifically need an FAA license, you might as well let it depend on the money.