Here are the actual MLB results for the postseason series from 1995-2012.
There were 126 series (I am not counting play-in games or 2012's 1-game wild card matchups - just LDS, LCS, and WS).
In 5 of those series, the 2 participants had the same number of wins.
In 61 series, the 2 teams were within 5 wins. The "better" team won 29 of the 61 series (winning percentage: .475)
In 37 series, the 2 teams were within 6-10 wins. The "better" team won 20 of the 37. (winning percentage: .541)
In 23 series, 1 of the teams won 11 or more games than the other. The "better" team won 14 of the 23. (winning percentage: .609)
Overall, the "better" team won 63 of the 121 series, for a winning percentage of .521.
I did not test for statistical significance of any of the above, but another way to look at it is that in MLB win differential is not at all predictive of postseason success when it is 10 wins or fewer. In the 98 series in which the teams were within 10 games of each other, the "better" team won 49, or exactly 50%.