As it relates to the equal golfers though...
I think the US player has the advantage and here's why.
1) If he's a long bomber and used to playing longer and softer courses, he's going to be much closer to the green with his drive in the UK.
2) If he also plays penal courses, this would also mean he's good at avoiding trouble like bunkers and is a relativly straight hitter, which is good for UK courses as well.
In the meantime
3) The UK player, who has relied on F&F to get him around links courses, is going to find himself with much longer approaches.
4) Additionally he's going to find out that the ground game isn't worth a hill of beans on the long soggy courses and his game will be under constant pressure to save par due to all those missed greens with the long irons in hand.
In the end I go with the %'s. Even though the long bomber has a lesser short game...he still has a much better chance at driving close to greens and at least getting the ball on the green with his approach shots, even if they aren't close, and being able to two putt for pars. In the meantime, the UK player will have much longer approaches with long irons and utility woods and will be under constant pressure to scramble and get up and down for pars.
In this scenario, I put my money on the US player given thier playing styles...and also assuming he's a 7 or 8 US capp and not a 10.
The professional tourneys seem to confirm this as well....far more americans can compete and be in contention in the Open, than UK players can be competitive in the US based tourneys. Until Padraig won the PGA in 2008, when was the last time a European won a major on US soil? It had been years and years and years.