I have and shoot both 300WM and 338LM. I shoot my 300WM much more than the 338LM, even though I have the time and place to shoot out to 2070-yards.
I bought a TRG in 338LM way before I ever imagined owning a 300WM. The 338LM is a fabulous cartridge, and very accurate. It does push you around some when shooting it, and almost prefer shooting it over a 300WM with the 230-gr Bergers as they push you around also. However, the 338LM really is meant for those real long distances. I have all the reloading gear, bullets, powder, primers, virgin brass, etc. to reload, but yet to do so as I have only fired around 300-rounds through my TRG. I have been told by a reliable source that the Finnish Defense folks swap out their barrels at 3K rounds regardless if they're still shooting well, and also change the barrel anytime the accuracy drops outside of 1-MOA. This tells me that they have determined 338LM barrel life to be just over 3k rounds, at least with the TRG.
In my 300WM's, I exclusively shoot the 208 AMax and Berger 215 Hybrids, I feel they perform for my needs better than any other bullet offerings in the .30-cal class. I don't load them hot, and at my altitude, they fly very well out to almost a mile. Barrel live I'm told is 2k with the 300WM. My oldest 300WM has around 1500-rounds through it so far, and with the throat hardly moving, and rifling still crisp, I fully expect to get 2500-rounds.
In the end, you really can't compare the two cartridges any more then comparing the 243Win to the 260Rem, both great cartridges, with both having pros and cons.