The leagues will likely always go back and forth, with the AL having an offensive advantage until the leagues conform their rules on the DH. AL teams can afford to throw big hitters bigger contracts under the premise that they can just stick them in the DH at the tail end of the contract. Pitchers would generally want to go to NL teams because it's easier to pitch against lineups with pitchers in it. AL gets really strong...better players want to go to the NL for a theoretically easier path to the World Series. If the NL goes and wins 10 straight ASG's and WS's then players will swing back to the AL.
I also have to imagine that NL teams have had higher draft picks based on their bottom teams getting absolutely smacked by AL teams. To add to this, AL teams throwing those big contracts at sluggers probably have given up more draft picks to NL teams than the other way around (maybe not by much, but if it's the difference between two AS caliber guys going to the NL instead of the AL...). This will also ebb and flow.