A 1/4 moa is a 1/4 moa, so regardless of the caliber a rifle that is capable of regularly producing 1/4 moa is not going to be any more accurate than another rifle in a different caliber that is also capable of consistent 1/4 moa groups.
I own several 338s and 50s that fit into this situation.
To claim 1 caliber is more accurate is ridiculous. 1 rifle/ammo combination may be more accurate, but then you are not comparing the same thing anyway.
The 50 has more reach than the 338, but how many can really make use of 3000 yards or more?
I find I can shoot more out of the 338s as the concussion from the brake is less than with the 50s.
I believe it is easier to be a more accurate shooter with a lighter caliber, but if the rifles and ammo are both capable of the same degree of accuracy, a skilled shooter would be able to produce the same results at the same distances with either to the maximum range of the lesser caliber.