Please save my life and do not be on my target at 600 or 1000 yards with either a 2 groove or a 4 groove Springfield. You will be all over the place and I will be worked to death trying to give you good pit service.
Military tubes are not target grade. I do not know what the accuracy criteria was for a WWII barrel, but I expect if it shot a bullet in the general direction of the enemy, did not blow up, that was all the accuracy needed.
Now I have shot in 100 yard reduced matches with a four groove A3 and a two groove A3. With 168 match bullets, they are equally awful. Barely hold the nine ring. I think the best I have shot was a 188. Both barrels will hold close to 2 MOA.
My load is 168 match, 47.0 IMR 4895, any case any primer.
I think the four groove barrel is a bit more accurate, but I can't prove to the nth degree.
I am certain there are a few military barrels that are better, but they are statistical accidents.
For cast bullets, the two groove was remarkably better.
With 180 grain bullets, the twist rate is 1:10 for both, so why should anyone expect one barrel to do better than another.
The American rifleman had an article, back in the 50's?, where two groove and four groove barrels were tested with ball ammo. I recall funny results, like the two groove barrel did better with armor piercing.