I know I've already argued this in considerable depth here, but watching Dominik Hasek make another deep playoff run makes me again wonder why Martin Brodeur is almost universally considered a better playoff goalie than the Dominator.
Hasek has a better career playoff save percentage and a better career playoff winning percentage than Brodeur. Only once in his playoff career has his team lost to an opponent with fewer regular season points (although the Ducks could soon make it twice). Brodeur has lost 5 times to weaker opponents, and he has been outplayed by average opposing goalies like Emery, Esche, Irbe, Ward, and Rhodes. Brodeur has been on three Cup-winning teams, granted, but in 2001 he was the main reason that New Jersey lost the Cup, getting totally outplayed in the Finals by Roy. Brodeur has never done anything like what Hasek did in 1999 in terms of being a difference maker on a mediocre team.
And those Cup wins? Cup wins are partly just a numbers game. Be on enough good teams, and eventually you'll win. From the time that Brodeur entered the league (the same time that Hasek became an NHL starting goalie) until the introduction of the shootout messed up the standings there were 52 100-point teams in 11 seasons. Nine of those teams won the Stanley Cup, so 100 point teams had about a 1 in 6 chance of winning it all. The odds were much worse for teams with less than 100 points: of all the teams that finished with less than 100 points in that time period, just 2 of them won the Stanley Cup (and one of them was New Jersey in the lockout season in 1995).
Brodeur has played on 10 100-point teams, so he would have been expected to have won about 2 Cups by now. He's won 3. This is the second 100-point team that Hasek has played on in his career, so based on that he shouldn't really have been expected to win anything. He won a Cup in 2002.
The number of rings doesn't matter - how well the goalie played does. Both Brodeur and Hasek have more rings than they would have been expected to win, given their respective teammates. Despite those weaker teams, Hasek also has the better rate stats (winning percentage, save percentage, etc.). The only conclusion, therefore, must be that Hasek's playoff record is better than Brodeur's.