The 300 wsm has a case capacity of 80.4 grains of water. The 338 Win Mag has a case capacity of 86 grains. A 338 WSM wildcat might pickup 2 grains by opening it up to 338. but that would still leave it short, by about 5%. All things being equal a 338 win mag should develop about 2-2.5% more velocity or about 60 to 80 fps at equal pressures.
Now if the 338 wsm is chambered in a typical short action, I would expect an even greater velocity difference, as match 338 bullets are fairly longish, eating up case volume.