Other than personal preference, I see no need for a premium bullet when using a 30-06.
For one thing, deer don't wear kevlar. Bullet weights suitable for elk and moose using conventional cup and core bullets start with the 180 gr. bullets and go up to the 220 gr. bullets.
Now I hunt elk with something a tad more powerful than the 30-06; a .300 Win. mag. with 200 gr. Speer Hot-core bullets at 2930 FPS from my rifle's 26" barrel. If I were to use the 30-06 for elk, I might use a 180 gr. Sierra Pro-hunter, which just happens to be my choice for Mule Deer in the 06. I also might use a 180 gr. Nosler partition, but that would depend upon the condition where I'd be hunting. The area I usually hunt elk is quite wide open and shots are on the long side which is why I prefer the .300 mag. However, if I drew an area where shots would be mostly much shorter range and possibly mainly going away type shots, then the Nosler might be my choice.
I've never shot a moose and probably never will. Just too darned old and it's gotten priced well out of what my pension will allow.
I think, based on what I've read that my choice of rifle would be my .35 Whelen and 250 gr. Speer Hot-cores.
With that said, I think I would stick with the 200 gr. Speer Hot-cores in a 30-06. According to friends who do hunt moose every year who use the 06, that's their bullet of choice. They see no need for premium bullets and I'll go with what they say based on their experience.
I'll just add that if I'm using a conventional cup and core bullet, I'll try for the heart/lung shot slightly behind the shoulder. If I'm using a "premium" bullet, I'll try to punch it through the shoulder to hit the heart and lung area. Seccondary fragments from broken bone can go a long way toward bringing a big animal like an elk or moose to bag.
All the above is just MHO.
Paul B.