Just looking at the calibers and grain weights. It's my understanding that the heavier a bullet is the less it will be effected by crosswinds.
I do know that higher fps will defeat crosswinds to an extent, but I was always under the impression that weight was the critical factor. The .50 is 2.4 the weight of the .338
True---Yes/No
the variables you need to consider are: Projectile weight, velocity, cross sectional area (front), cross sectional area (side), wind speed & direction, and gravitational pull
bullet drop is a direct relationship between velocity and gravity, but larger diameter bullets (with the same initial energy) lose velocity quicker due to wind resistance
bullet drift is affected by velocity, weight, and wind speed/direction as well as the side area of the projectile (more area, more for the wind to grab)
the trick is to keep the velocity up as long as possible so there isnt any time to drift or drop, which means for long range accuracy you need as much initial energy as possible
at ranges over 1,000 yards the .50 BMG has a definite advantage, partly due to its greater weight, but also due to the greater energy it starts out with, but a .50 case necked down to take a .338 projectile would be better than either the .50 or the .338, as it would start with the same energy as the .50 but would move a LOT faster
if you look at all the non magnum military & commercial calibers smaller than .338, almost all of them have a point blank range (bullet drop + - 3") of between 250 and 300 yards
comparing the .223 with a point blank range of approx 275 yd and the .308 at approx 285 yd, if wind is an issue id go with the .308 because at that range the velocities are very close & the .308 wont drift as much due to its greater weight (generally 55 - 62 grains for the .223 vs 145 - 180 grains for the .308)
but then you get into the argument of heavier bullet / more energy / more kick / bigger weapon / heavier ammo load / etc. etc.