Tbone - The 300 WSM no doubt is a great cartridge. But I think you may be kidding yourself if you think you can get it to run along side the 338 Win Mag. It will be more comparable to the 300 Win Mag.
But IMHO, there aint no deer in the world that would know the difference if it was hit with a bullet from your old '06 or the 300 WSM.
I'm sure your 300 WSM will serve you well and I wish you luck with it. But me, because I have a 30-06, I opted to go one notch higher and got the 325 WSM. And I love it.