When I left the US for the UK my handicap was 1.1. While spending 18 months in the UK, it was 2.4-2.7. When I returned and entered my first scores it was 0.3, and then progressively dropped to +1.6. I found it more difficult to get the handicap to drop in the UK. It was all tournaments (fewer scores and tougher conditions, especially for big club events), and the SSS was always around par or better.
One of the courses that I play regularly in the US has a rating of 75, so it is quite easy to maintain a lower handicap by shooting rounds just over par. I think that US handicaps are influenced much more by the course you play the most rounds at than in the UK. I think that ratings have a wider range than SSS do.
In my experience, I would expect the UK player to win the majority. I also found that handicaps in the UK are more accurate (excluding the few bandits every club has). Nearly all the matches I played with handicaps up to 22 the proper amount of shots were given. Only on a rare occasion of very good play by one side accompanied by very bad play on the other did the match not make it to 16-18.
I think that most handicaps in the US are way off. I have also found that people in the US think that your handicap is your average, which it is not. It is your potential, and you should only shoot your handicap or better about 30% of the time. I play in too many matches were people will say I'm a 10. Later you find out that they average around 81-82, which would make them more of a 6-7 in the US.