In my opinion the 338 win mag is best suited with the lighter bullets such as the 225 Nosler AB which has about the best BC in the 200-225 grain bullet range. It will shoot the heavy bullets accurately but within the optimum effective range of the 338 win mag I think you are best with the faster lighter bullets.
The 300 grain SMK will kill stuff just fine out of your 338-378 wby at any range you can hit it.
Predictions are difficult, especially when they involve the future
Then there are the guys who sing the praises of the .338 Whisper....
When you are launching a .800 Ballistic Coefficient bullet does the velocity really matter all that much?
When a 300gr bullet with thick target jacketing impacts living tissue at anything near 1000 fps, the blow is almost sure to be a mortal one.
Question is, do you have the twist rate to stabilize the 300gr bullet? If so, go for it. Otherwise, why not shoot a .30-06 with 200gr matchking and get the superior performance of a higher BC bullet?