Actually, the presence of a DH doesn't give more strategy. It just gives a different type of strategy. In the American League, the manager has to decide before each game which of their players they will use as the DH that day, and which ones will go in the field. If your good hitter is a catcher, you really can't DH him because then he wouldn't be able to go in the field later in the game without the manager then losing his DH. So do you DH your good hitting catcher to give him a half day off, or do you bench him and give him a full day off barring any injury to the backup catcher?
Also, the manager has to watch his pitchers a lot more closely than in the NL. In the NL, if your pitcher is pitching an okay game and the bottom of the 7th inning comes and he is due to bat, the lineup pretty much dictates when to take out your pitcher. In the AL, it's the actual performance of the pitcher that dictates when he is to be removed from the game. Take a look at Game 7 of the 2003 ALCS. If that were in the NL and Pedro was due up in the bottom of any of the innings before his meltdown, then Grady Little probably would have taken him out of the game since the lineup forced him to. Instead, Little had to try to decide for himself if it was time for Pedro to come out and to all Red Sox fans out there, he made the wrong choice.
So while the strategies certainly aren't the same, the presence of the DH doesn't really take away any strategies. It just changes what those strategies are. I think there are pluses and minuses in both leagues, and to be frank, I like that it's different. If it wasn't, then we wouldn't have all these threads to debate the merits of it in.
