Without doubt, the 300 WinMag. has more recoil than the 308Win. However, as noted,
various factors come into play here including the weight of the rifle, and the stock design. All else being equal (weight, design, etc.) the 300 Win.Mag has far more recoil
than the 308 Win.
Stock design will have a big role to play. The older/classic style of stock is generally far better (ex.: Ruger 77 MKII). The recoil forces (ft.lbs) tends to push back in a straight line - into the shooters shoulder where it belongs. Monte Carlo stocks (ex.: Rem.700BDL) not only push back, but also upward - like taking a jab in the cheekbone
each time you shoot.
Watch the amount of drop in the stock design/measurments. The less drop (straighter stock), the less the percieved recoil will be.