I've fired both 308 Win and 300 Win mag target rifles in competition. The 300 Win mag is significantly more difficult to shoot as accurately as the 308 Win due to the increased recoil. Age and joint deterioration have taken me out of the 300Win mag comfort zone and off the firing line but I still shoot the 308 Win when I really want/need to hit something(within it's range capabilities). My old 300 Win mag rifle weighed over 11 pounds making it much easier to shoot well than a hunting weight rifle but the 308 I'm shooting now weighs 10# making is a pussycat to shoot.
I'm glad someone cleared up the caliber vs cartridge confusion so I didn't have to.