Garand is the Canadian that invented the 'best battle implement ever devised' according to the best General ever devised, General Patton. And the M1 Garand is the precursor to the best battle rifle in existence, the M1A aka the M-14. (you don't need automatic fire. let your machine gunners do that for you in battle. the semi-auto version is fine.) Mr Garand didn't produce much else of fame and note, but why would he. He made the absolutely best rifle EVER.
Browning is ok, I guess. He did invent a few things.
What am I saying?!!! He invented the best handgun, ever, the 1911 .45, the best Euro-Pellet-Shooter, the Hi-Power, the best heavy machine gun, the Ma Deuce, which is only now being considered for replacement in some applications because it is too heavy to carry by hand. (What is wrong with soldiers today that they can't carry an 85 pound machine gun like it was nothing? Sheesh.) He invented 7 pistol cartridges. A boatload of very nice lever action rifles. One of my favorite light machineguns is the Browning Automatic Rifle, used extensively by WWII soldier and SHOULD have been issued to WWI soldiers.The Winner?
Garand is inspired on that one superb weapon, but you gotta go with Browning for his exemplary and HUGE body of work. Browning is the victor, but I'm sure both men would shake each other's hands before the cage match started and after it concluded when both were bloodied and missing teeth. They'd of course return any teeth that wasn't there but was embedded in their knuckles. AND they'd buy each other beers at the bar across the street. (Well, maybe lemonade for Mr. Browning. His faith frowned upon alcohol consumption.)