I don't think there is any support for the NL vs AL debate overall.
The opposite thinking of a DH making one more spot in the rotation harder is that the pitcher not having to swing a bat and possibly run bases can rest their bodies between innings.
The batting average for the NL is .252, for the AL it is .247. So you could say that the NL would be harder since they have the higher batting average.
The DH was introduced in 1973. Since then here are the break downs:
51 - AL
54 - NL
Perfect Games Since 1973
9 - AL
5 - NL
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