Here's yet another reason to get rid of the DH--league disparity, and part of the large advantage the AL enjoys over the NL. You may ask why it gives the AL an advantage over the NL when the teams play with the same rules. The answer is: personnel. The NL teams don't carry that extra slugger that the AL teams do. As a result, when they face one another, you see teams like the Marlins playing a player like Jason Wood when they require a DH. That's not to say Jason Wood was the DH--on the contrary, that task was left to Miguel Cabrera. Aaron Boone played third, and Jason Wood and his .239/.286/.368 line spent the game at first.
Overall in Interleague games, despite players like Miguel Cabrera being at the DH spot and counting in this statistic, here are the stats:
AL DH's: 467 AB, .315/.412/.503, 87 R, 20 HR, 97 RBI, 2 SB, 1 CS
NL DH's: 505 AB, .273/.347/.444 67 R, 19 HR, 63 RBI, 4 SB, 2 CS
That's a huge differential. The NL DHs were responsible for 38 more outs. The AL DHs drove home 34 more runs and scored 20 more times. That's 1.5 games worth of outs and an average of .41 runs per game. None of this counts the at bats of the Jason Woods who had additional at bats during that game, either.