I don't have any evidence to prove it, but I know wqhd hardly affects battery. I can see 120hz making a dent though. I'll probably never know the difference, because I don't plan on switching to 60hz.
I actually turned off 120hz not because of battery but because it's to fast for some things. Actually hurts my eyes when scrolling through web pages. The 60hz on this phone with the 240hz touch response is still incredibly smooth and fast.