Actually it's the opposite, if you never watched the players play you would probably pick the one with the better resume on the big stage. However if you did watch them play, you might realize who the better player was. If you had to take one goalie on their best day to win one game, I think Hasek is the answer.
Don't confuse team success with the individual talent level. I agree that Roy is definitely neck and neck with Hasek, as is Brodeur and a few others. One of the problems with these arguments is when people use terms like "easily better" or "AINEC", because that implies one goalie is great and the other is not, or that there's a wide gap, when we're actually talking about a few millimeter's difference at the end of a marathon.
But we aren't talking a few millimeters at the end of a marathon, we are talking a large gap. And if you've watched how on earth could you take, for example, Roy's 86' post season run and compare it to Hasek winning on Detroit in 02'. Now if you have indeed watched you'd know how different from each other those performances are and save the millimeters commentary. One was amazing in the regular season and one was amazing in the post season, so it then becomes which of those seasons are more valued and reflect upon a players greatness more... Which is an easy answer.
So let's look at his Cup in 02' (his other Cup he only played 4 games). He was on a Detroit team that was 51-17-10-4 and who's playoff squad included Brett Hull,
Shanahan, Fedorov, Luc Robitaille, Yzerman, Larionov, Holmstrom, Datsyuk, Draper, Lidstrom, Chelios. Hasek faced an average of 24 shots against and the finals vs Carolina the only game he faced 20 or more shots had 6 periods in it.
In 02' Detroit was 1st in the league, Hasek faced 24.4 SA/pGP - .920%
In 86' Montreal was 8th best in the league, Roy faced 25.3 SA/pGP - .923%
In 93' Montreal was 6th best in the league, Roy faced 32.3 SA/pGP - .929%
In 96' Colorado was 3rd best in the league, Roy faced 29.5 SA/pGP - .921%
In 01' Colorado was 1st in the league, Roy faced 27 SA/pGP - .934%
In each of Roy's Cup wins he faced more shots on average and put up better numbers, on three of those teams they were inferior than the one Hasek won on, and when Roy was on a 1st place team it was just the year prior to Hasek winning and Roy's numbers dwarf his on a similar caliber team.
But Vezina's and Hart's and such, which is valid, anyone wants to argue Hasek's better than Brodeur and I wouldn't say anything, Roy on the other hand was the Goat.