I've flown both a few times and in my opinion very little difference in hard product.
AA as with all US carriers can have inconsistent service - some crews great, some clearly don't want to be there. Japanese carrier crews are very attentive and very consistent but at times seem a bit formulaic.
I like the AA food but I'd give an edge to NH.
You wouldn't get in so late as to not have public transportation options in NRT if you took the NH flight.
If you can afford it and aren't going to fly a lot of international F to Asia in the future, I'd seriously consider it - just for the experience factor of a carrier you probably won't fly on again.
Is it otherwise a few hundred dollars better? Probably not, but I'd be a bit annoyed if I had a indifferent crew and decided to go with AA.