From what I gather, the M1 is a more accurate rifle and the 7.62x51 is a more accurate cartridge. To get the best of both get a M1 with a 7.62x51 barrel - that is if you're serious about paper punching.
LOL...In these two rifles in question, the 7.62 is the more accurate cartridge. It's largely due to the limitation in powders for the gas system. In short, you can't get close to 100% loading density in a 30-06 used in a Garand.
The rest of the statement about the Garand being the more accurate platform is probably not true from a competition standpoint. Bart Bobbit and Joe Sopko will tell you the Navy's Garands built by Mac McCoy were the most accurate Service Rifles on the line...but the Navy wasn't winning very often at the Nationals. The Army and the Marines Service Rifle Teams shot the best scores ever shot with a 30 caliber service rifle, but they both shot M14's once the accurizing was worked out.
Bottom line...shoot what makes you smile the biggest!
