Which league hits better (if you exclude the number-nine slot?)

Answer: They're virtually identical.

Here are the numbers for 2006:

What it comes down to then is that the effect of the American League using the DH shows itself pretty much entirely in the number-nine slot.

Pitchers hitting is the primary reason for the low National League figure, of course, but they aren't batting as often as you might expect. The number-nine slot came to the plate a total of 10,033 times in the NL in 2006. NL pitchers had 5,684 plate appearances last year (regardless of lineup slot). That means that pinch-hitters (and double-switches) accounted for nearly half the plate appearances in the NL ninth slot. When I first saw this number I was surprised, but I scanned a few boxscores and saw that it was not uncommon for an NL starting pitcher to bat twice and then have pinch hitters bat once or twice more later in the game.