First things first. Phyrrus - neither of the organisations that you list offers integrated training, indeed no US based organisation does. The best that you can expect is 'structured' modular training, whatever that means.
The fact is that there are, for whatever reason, JAA airline recruiters who are biased against US (or any other non-JAA) training, they may not be many but they do exist. There are also UK airline recruiters that are biased against any non-UK training and, I assume, Dutch airline recruiters that are biased against non-Dutch training, etc. However, there are no JAA airline recruiters that are biased against JAA training, nor UK airline recruiters that are biased against UK training. Therefore, by electing to complete training in the US you may (and probably will) reduce slightly the number of JAA airlines that will consider you for employment - this may or may not be significant. On the other hand, your flight training, if completed in the US will consume slightly less cash than it would in most (but not all) of the JAA.
Florida Mud Wrestler so obviously has a vested interest in US based training that his/her opinion is totally predictable and should be considered accordingly.
rhovsquared, apart from being doubly dynamic, is clearly a complete prat with nothing sensible to contribute. You will, unfortunately, find a surprisingly large number of these in the industry - mainly working as instructors in the less reputable flight schools.