I like this thread, so I'm going to chime in with my two cents (and that's exactly what it's worth).
I have witnessed the best players at all three games for quite a while now, and have come to this conclusion. And I'm not going to go into specific reasons why I feel this way. Remember it is just my opinion.
Among the cue sports, Three Cushion Billiards is the most difficult to master. Snooker is second and Pool is third. Sorry if I offended anyone but that's my observation.
That being said, I have yet to see ANY player who is a champion at one discipline, switch to another and excell! And I'm leaving Allison and Karen out of this because they have not excelled against the best players (just the best women players) at either of their chosen disciplines. They're still pretty damn good in my book.
Yes, it's true, some former snooker players have become very good pool players, most notably John Horsfall from Canada, Steve Davis and Tony Drago. But champions, they are not. Same goes for top pool players who attempted Snooker. Jim Rempe and Steve Mizerak come to mind.
Now there is one man who actually did cross over and become a champion at more than one cue sport. Do any of you know who that is? I'll let you guess for a while. I'm sure Terry knows. So you don't get to guess. And this man may have been the one American guy who could have gone overseas and played high level snooker too. If he had so chosen. He was truly unique, kind of the Jim Thorpe of cue games.