While I'm fairly biased; I'm going with the cardinals to win this one for a couple of different reasons.
1) The Rangers offense is amazing at ranger stadium, but hasn't traveled all to well throughout the regular and post-season. Combine that with the fact that they are going to have to bat the pitcher at Busch and that further diminishes it's away offense. Meanwhile the Cardinals, looking at every team's road games (no home games), had the best road offense in the majors. The batter friendly ranger stadium and the introduction of Allen Craig in the DH will only improve upon that. Craig has 12 homers in 218 at-bats. "The home-field advantage for the Cardinals isn't because they get to play at Busch, it's because Texas has to."
2) The Cardinals are not a pitching staff that is going to straight up challenge hitters (much like they saw in Detroit). They are not going to throw inside fastballs nor are they going to try for strikeouts. This is primarily a ground ball pitching staff (thanks to Dave Duncan) that isn't going to give Texas a lot to hit.
3) Ron Washington is a damn good manager, but Tony La Russa is simply better. In a 162 game regular season the Rangers win, but in a best of 7 the better manager almost always wins. That is La Russa.
4) Yadier Molina. The rangers have a lot of speed ranking 3rd in the majors in stolen bases. It hasn't been a major part of it's offense, but it has been a part of it. Molina simply shuts down any teams running game. Another small blow to the rangers offense.
P.S. Here's a little nugget of trivia for you. By the time baseball got to Arlington the Cardinals had made 12 world series appearances.