If the twist rate of the barrel is appropriate for the bullet, I don't see where one would be more accurate than the other. With a .277 bullet that's weighing the same as one of .257, you'd wind up with problems at long range since the shorter and fatter bullet would lose velocity faster. I'm thinking of wind drift, which of course is an external factor.
Probably better to compare bullets for each caliber that have the same ballistic coefficient, to really have a fair test.
Art