I would go for the FAA and later conversion route. There are quite a few advantages to learning in the US, not least the flying 'in the system' which in general is sorely lacking in European flight training. Others are night VFR and generally more training to use the nav instruments.
I don't know if and how EASA will impact the conversion process, under JAR it was pretty painless. Air Law (which you'll need anyway) and Human Factors test, then the checkride and - at least in the UK - the radio license.
There's one more advantage to doing it this way - you end up with two standalone licenses. This can be a huge advantage, especially if you want to validate one of them somewhere else in the world, as the FAA is usually much, much quicker in replying than most European CAAs (and I don't even want to think about response times from EASA, if it's them who do this in the future).