There is no hope for a One X on Verizon, that ship has sailed. Yes the screens are the same for both phones, but as you stated the resolution and PPI (pixels per inch) favor the rezound pretty handily.
I would put my dual core, 1.5 ghz, sense 4, ICS Rezound up against the inc any day. It would be close.
SoC will help battery...no doubt. The batteries themselves are basically the same. I wouldnt doubt that the inc battery would fit the rez as well since they have close to the same form factor.