I think the genetic evidence is adaptive mutations that are present in all humans

Our species also engaged in cannibalism.

That isn't evidence that we killed the Neanderthals for food. Rather than, say, having added some ecosystem stress through competition that left them less able to handle a major volcano 40,000 years ago.

I think that if human practiced widespread and consistent cannibalism, then it stands that we likely ate Neanderthals and other homo species to some degree