I think the problem with Aki-P giving the goood songs to Nogizaka is simply that AKB can't make them work, or at least not as good. AKB is more fanservice, with bikini singles and revealing outfits, and not too many good singers. Nogi, on the other hand, has more of a "princess" image, with bikini shoots banned (except very few exceptions). Plus, as you said Nogizaka is only raisimg while AKB is slowly fading (despite management desperately trying to avoid it)
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