As ADNA said, stock fit is critical. Anything that doesn't fit can hurt. A well fitted stock that doesn't bash your cheek, is made so recoil goes straight back to your shoulder and has an adequate LOP with a good pad will do a lot to reduce felt recoil.
Assuming that the two rifles are of equal weight, a .338 WM firing a 225 grain bullet will generate more recoil energy than a .30/06 firing a 180 grain bullet.
The trajectory of the .338 WM loaded with 225 grain bullets is comparable to a .30/06 firing 180 grain loads.
I have two .338's. One is a full custom built on a pre '64 M70 action with a Swarovski Z6i. It weighs about 9lbs loaded and recoil is not bothersome at all.
The second is a Blaser R93, also with a Z6i that weighs about a pound less. The Blaser has less perceived recoil than the M70. Go figure.
The .338 WM is a great cartridge and is excellent for PG. My standard load is Federal factory 225 grain TSX's, which shoot less than an inch in both rifles. For leopard, I use a 225 grain partition.
Of late, I have begun to wonder whether all the sturm and drang of more potent cartridges is worth the bother. In my personal experience, given a well constructed bullet and PRECISE SHOT PLACEMENT, a .30/06 will kill them just dead as anything else. Except for very specialized use, a .30/06 and a .375 are really the only two rifles a hunter "needs". Another good pairing for those who have Africa in their plans and can shoot them accurately is the .338 WM and the .416 Rigby.
