If recoil is your only concern, than go with the 06. I have killed one elk with my 06, but wouldn't mind having a mag. I am thinking about getting a .325 WSM
I have shot my 06 and my cousins 300WSM a lot lately, getting ready for some hunts. I notice no difference in recoil between the two. It has been said that the short mags have less perceived recoil than standard mags and that may be true.
It could also be the gun design. My cousins 300WSM is in a model 70 classic stainless with the synthetic stock and it is not uncomfortable to shoot at all. That combo definitely is flatter and harder hitting than the 06, so it may be the way to go if you want the power without more felt recoil.
Definitely stay away from the weatherby 300 if you are concerned. The muzzle blast is fierce out of those things. To me muzzle blast is worse than actual recoil in making people shoot bad. A great example is a little .243 mod 70 featherwieight we have. Its short barrel really has some muzzle blast when driving light varmint bullets, but little recoil. My wife prefers shooting my 30-06 with 180 Barnes X to the 243 with the light bullets. Obviously the 243 is not recoiling nearly as much, but he blast scares her, even with good ear protection.
Best thing to do is go to a shooting exibit or range that lets you test fire different combos of gun/cartridge. Find a 300 mag combo that you are comfortable with and you will have a superior Elk gun to most 30-06s. I just like the idea of having a little more punch than the 06 can provide, especially for big bulls. Those animals are so tough, a little more can't hurt. If I continue using my 30-06, I will always keep the range well under 300 yrds and much closer if possible.
I recently went to a show and shot all kinds of combos including .338 mags, 375 mags and 458 win mags. It is amazing the difference in felt recoil with different combos. I shot a savage .338 with muzzle break off the bench several times that was not bad at all. Wouldn't want to shoot that cartridge in the wrong gun though.
Still, what the 06 gives up to the 300 mags is probably very small for most species and shooting situations, but I like having more power if I can handle it for bigger game. Just would give me a little more confidence, especially when the big bull elk of a lifetime steps out at a little over 300 yrds.
Good shooting,
Brian