Using default OAL and case capacity settings and 65K PSI in both and I plugged in a 26in barrel QL projections show there's only around 40fps difference between the 300 WSM and 300 Win and I ran the numbers using both a 200gr and 212gr bullet. RL26 was listed as the top performer with regard to velocity for both and the 300 Win uses 6gr more powder.
Both shot at the same rate of fire, loaded with the same or similar burning powder/s bullet combo, and taken care of the same, I don't see how one would have any significantly longer barrel life than the other. Maybe if you were running something like N570, which tends to be a bit harder on throats, in one and H1000 in the other, maybe, you'd see a greater difference but everything being equal I'd be hard to sell me on one having less barrel life than the other.