The answer to your question is a couple of hundred feet per second, is that substantial, probably and it can sure come in handy on ocassions..My 300 H&H with a handload shoots the 220 gr. bullet at the same velocity my 30-06 shoots a 180 gr. bullet..for a stopping shot I think its worth the difference. I like them both, but I know which one is the most powerful and which one shoots the flatest and the 30-06 is my favorite cartridges, but its not a 300, end of story. Enhanced ammo you say? that won't work, Enhanced comes in both calibers!.
Phils latest bruha with a Big Alaskan Brownie took place a few days ago with the 30-06 and the 220 gr. Nosler..Bear came at him in the thick alders from 15 feet, first shot between the shoulder blades put him down, then he gets back up, second shot in the neck and he goes down and gets back up, 3 rd shot in the neck and it kills the bear..Good performance from the 30-06, but Phil told me he was wishing for his 458 Lott, that is too close for comfort, not saying the 458 would have done a better job, but it would have made Phil feel better!! I have been charged 3 and a half times by Cape Buffalo and I always wished I had a bigger rifle, even though I had a 404 or 416 Rem..it's a natural reaction, even though the rifle you had worked.:)
The bottom line is a 300 is bigger and better than a 30-06, a 338 is bigger and better than a 300, a 375 is bigger and better than a 338, an on up the power scale, thats the way it works, like it or not but some just can't seem to understand this simple principle..If your satisfied with what you got then your good to go, and the results are yours to live or die with I suppose...I'm good with that anyway.
