I don't know to whom you have been speaking, but the 300WSM is here to stay. It is flat shooting, hits hard, is accurate and can fit into a nicely compact, short action rifle. It can be considered an ideal caliber for all North American big game. I own one, a Remington Model Seven, and I love it.
Having said that, there hasn't been a caliber introduced in the last 100 years that will replace the '06. I have owned lots of them over the years (45+ years of hunting that is), and I will tell you that there isn't a thing that it can't do, and do well.
But there ARE differences in thes two calibers. Ammo for the '06 is much less expensive and always easier to find. The 300WSM does shoot flatter and hits harder, but does "kiss" your shoulder a little harder too. If you like the shorter actions rifles, (I do because I'm a short guy) with slightly faster handling, and aren't bothered by the increased recoil, you might be drawn to the 300WSM.
Anyway, that's my take on these two fine calibers. If you can't make up your mind, just toss a coin and you will have a GREAT rifle whichever one comes up. If you are considering either of these, you are smart because you simply can't go wrong either way. Good luck and great hunting!