Standard muzzle velocity for the 300 Win. Mag. with a 180 grain bullet is 2960 fps. For the 300 H&H is about 2880 fps. As such, the muzzle velocity is relatively close between the two.
Keep in mind, however, that handloaders can increase (within safe pressures) the velocity of each round. Specifically, if you go to cpcartridge.com, you will see that, for the 300 H&H, they have the muzzle velocity set at 3000 fps, which is actually MORE than that of the 300 Win. Mag.
Zachary