I have a Tikka 270 that I'm looking to re barrel into some type of 6mm Nuclear cartridge too. Not picky on barrel life. I want smooth cycling and flat trajectory. Some PM members suggested the 22-243. The 243 SLR, or the Competition Match, 6x47 lapua, 6xc, and on, and on.
Like others have said. Just put them all in a hat, pic one, and ride with it. For me, the 6mm-06 looks the easiest. The 6BR's types might have cycling issues, (or not). I have never had a rifle that cycles as smooth as this Tikka. I am in no rush. Bix'n Andy still hasn't made a two stage trigger for it yet. Im going to shoot my 270 barrel out first with the 110 Vmaxes, 110 pro hunters, Game Kings, or Berger's.
No pd's for me. Im Just sniping coyotes at distance. I have never had a 6mm Rem, but I would just go with that, unless you want more of a challenge. I have been asking myself the same question, and I have yet to make up my mind. Have fun with it! I know I am!