Having shot both the Garrand and the 1903, I hate the 1903 fine little notch sight, and much prefer the Garand peep sights.
I have both, though my 03 is a 03A3, and totally agree the Garand sights are much better, even to the peeps on the 03A3, the front sight being on the fine side and rather easy to damage.
Recoil is not a huge amount softer, but noticeably so with the Garand, also.
But with my sample of two, one each, the 03A3 is slightly more accurate. I shoot the same exact load in both, and they both have Criterion barrels. I still kinda favor the M1 but enjoy both quite a bit.
