.308, 30-06 and 300 WM will shoot the same 30 cal bullet, to certain degrees.
the kinetic energy that creates knockdown power is based on velocity and weight of the bullet,
given that all 3 cartridges shoot the same bullet to different velocities, they should perform the same way at different ranges, more or less.
The 30-06 is about 200 fps faster than .308, and 300 WM is about 200 fps faster than 30-06.
They all loose about 200 fps velocity every 100 yards.
So what the 308 does at 100 yrds, the 30-06 does at 200 yrds, and the 300 wm does at 300 yrds.
Basically each step up in cartridge gives you another 100 yards of effective range.
If your moose hunt takes place in dense woods at close range,you probably won't need the longer range capability,
so it all depends on the situation.
For me though, I'd prefer not to limit myself.
Where I hunt, I'm more comfortable taking my '06 or my 300 WM, loaded up with a premium 180 - 200 grain bullet.
I don't want an animal running away after it's been hit.
For moose, I use a "heavy for caliber" bullet, preferably a bonded core or copper bullet.
If you're comfortable hunting moose with your .308, and you can put the bullet where it counts, good luck.
I know of an "old timer" who has shot dozens of moose with a 300 Savage, and who knows how many have been killed with 30-30's.
Then again, some guys swear by the 7 MM or even the 338......