I'm sure you meant .243 rather than .234 vs the .257 Robt.
personally, I prefer the Roberts. You can go with bullets as high as 120 grains if you go with a 1 in 10" twist. That wouldn't be a problem with the lighter bullets. I think that if I were doing a custom Roberts though, that I would look into a 1 in 9" twist for the heavier bullet. My Winchester M70 Featherweight has I believe a 1 in 10" twist (I ought to check it out one of these days) but it's marginal with the 120 gr. Speer Hot-Core. It is dead nuts accurate though with just about every 100 gr. bullet I've tried and excells with the Barnes 100 gr. TSX.
I have a couple of .243s as well but I'm not all that fond of that cartridge for fairly large deer like Mule Deer. That's based on seeing big Nevada Mule Deer shot with the cartridge, none by me BTW. When I lived there, I had access to several private ranches and would guide kids on their first deer hunt. They used my rifle which was a .243 and in all cases the shots were well placed. Only one deer was a bang flop/DRT. All the others rans some distance from maybe 30 yards to one very dead deer that went over 200 yard. Dunno what was keeping that one up but he ran until he hit a fence, backed up and hit the fence again and then did it one more time and then dropped. a couple of those deer went far enough without any usable blood trail that, if the area had been very brushy, odds are some of those deer might never have been found.
So, my choice would be the roberts.
Paul B.