You have stated these two hypotehtical players are pretty even in play.
What else is there? Gambling experience does not provide a magic edge, lead, or charm. Playing experience does that.... and these players are pretty even... right?
Gambling experience may help confidence - maybe the ability to fade some bad rolls - but it can't make one single ball. The only exception I can think of is when one of the players is out of thier comfort zone (high rolled) and the other is not. Don't bet outside your comfort zone ever - or you will be thinking about your wallet instead of your stroke.
If the two players are even in play - I would give the edge to the guy who wants the win more for whatever reason.
Generally gamblers have an ability to match up a bit better - but your thoeretical guys are pretty even right? The match is made. Now it's time to shoot. I truly enjoy those "even" kind of matches or sets. Nobody has the nuts - and you have to really play to win.
For some reason - those matches used to be a lot easier to find. If you can get one now - jump on it. An even game - wow -
EVEN matchups are a MYTH! lol