All the serious match shooting up to WW2 was done with the M1903, not the O3A3 which was a war baby. Match shooters used the aperture in the rear sight leaf. After WW2 the Garand displaced the M1903 because it was the official service rifle.
I've pulled some nice groups with the aperture in the M1903 leaf, but that's not to diminish the 03A3. The M1903 aperture would be an inferior combat sight than the 03A3 rear sight because its very small, making it hard to pick up a target in field conditions.
Both models are easy to set up for good shooting; solid contact between the recoil lug and the stock, clearance at the rear of the upper tang, barrel free of contact with the stock except at the forend tip where you want 5-7 lbs pressure. There must also be clearance between the top of the barrel and the upper band. One really nice thing about the M1903/03A3 is that it has a fairly heavy barrel, esp when compared to the Garand.