While you may hear this claim and that claim in favor of one or the other, most are symantics.
The WSM works in a short action, but I have never felt the long action was any real disadvantage.
The 300 Win Mag does have a redundant belt, but works fine despite this "anomaly" lol.
Accuracy difference? More likely an individual rifle thing than the chambering. The 300 Win Mag has won many long range contests.
Recoil, that has been debunked many times. The 300 H&H and the 300 WSM have basically identical capacities.
In equal weight rifles at identical velocities, recoil is also identical.
For the dedicated reloader, the 300 Win Mag has slightly more velocity potential, as a rule. Again, individual rifles vary.
I personally believe the 300 WSM is slightly more "finicky" to load for, [I own both chamberings], FL sizing the WSM case can be touchy.
Bottom line, buy the one that you like best! Both will serve you well as long range "Thumpers"
Regards, Dave.