Oddly enough, I think a high powered .22 such as the 22-250 using heavy bullets might make a fine sniper rifle if the twist was fast and the bullets were say 70 grain.
For that matter about any high powered rifle using heavy bullets of great sectional density and good ballistic shape should do fine.
One of the reasons the 6.5 Swedish Mauser did so well in long range shooting is because they loaded them with long heavy bullets with a fast twist.