Sudden encounter.

In character.

Win By Death, K.O or Surrender

This is a tough battle but considering whose fighting we can toss out surrender. Ultimately I would say RB Doomsday wins. For the following reasons. RB Doomsday seems to be able to put together some (although rudimentary) forms of strategy. And considering what he's fighting this is any edge that will help. Two remembering the stories base starting strength seems to be higher. (Also pulling from the Superman annual where it gave the impression RB Superman was stronger than 52 Superman because he was draining enough solar radiation once he became active to endanger the earth). RB Doomsday had already adapted beyond a head on fight with Superman. And while 52 Doomsday did hold his own when it was clear he did get splattered. We've barely seen RB Doomsday get a bony protrusion broken. Overall I believe the RB Doomsday would overwhelm the NEW 52 Doomsday causing him to use his assimilation technique but I don't think it would matter as Doomsday is Doomsday and he wouldn't be affected. Also supposedly the New 52 Doomsday was fully matured and his previous form which seemed to be more like the RB Doomsday was his infant form. But RB Doomsday never got beaten to the point he had to assimilate. If you had that kind of power you were something that couldn't be overcome anyway.