Well, let's think about it this way...
Your AL team and NL team are all composed of 25 players: 5 SP, 7 relievers, 8 starting position players and 5 bench guys. In the AL one of the bench guys is the regular DH. All your SP have 3.00 ERA, your relievers all have 3.50 ERA. Every single position player and bench player have .300 batting average.
If we are arguing on the basis of all things being equal, in the AL park, both teams will have an equal lineup against equal pitching with DH's that have equal ability. In the NL park, DH is now on the bench and both pitchers suck at hitting. Both teams have to play by each others' rules and must adapt to the perceived advantages or disadvantages each league confers.
However, we know that all things are not equal, and that starts with the way teams are constructed. The AL will not usually go with DH by committee and will employ one guy (i.e. a David Ortiz) to sit out half the game and hit the snot out of the ball when he is up. The NL will not employ that same guy because it's a waste of money to have that good of a hitter on the bench when they can have a utility guy as a defensive replacement. If they had a guy like David Ortiz, they'd either trade him to the AL or play him in the field (most likely at 1B).
The only reason we NL/Cubs guys are talking about inequality is because the game is unequal. Even if the AL team is missing their DH, their lineup and pitching outshines the NL, thereby removing whatever perceived disadvantages they might have for sitting their DH. The NL guys may have some advantage from replacing their pitcher with someone who theoretically could hit, but you're basically replacing a #9 hitter with a slightly better #9 hitter. The advantages/disadvantages are not as significant as you might think.
