I've always found this classification interesting, as the '03 and Mauser were so closely related. Better sights on the Springfield, I suppose.
Had the Swiss not been neutral during WWII, I suspect that their K31 would hold the "best target rifle" honors. It was really designed more like a light target rifle, disguised as a service rifle.
The 03-A3 has a much longer sight radius than the Mauser due to the provision of a receiver-mounted sight. The original 1903 is much the same as the Mauser.
Correct about 03s & Mausers being closley related. Mauser
sued the United States Government for patent infringment. The U.S. Government paid royalties to Mauser until the first world war.