I voted .308.
Cartridge cases don't kill game.A 30 cal bullet delivered at a velocity the bullet was designed to perform with will do the job a 30 cal bullet will do.
Because we have better bullets,both BC and bonded,a 165 is now(according to me) adequate for elk.I'm more of a 180 to 200 gr guy,but I concede a 165 works,and works well.A 308 will deliver a 165 with enough power for elk at 300 yds,assuming a well placed heart lung shot.
Dead is dead.
Myself,I think inside 300 yds is a good idea,and it covers maybe 90+% of the shots one is likely to have.
Maybe 5% or 10 % of the time,a .300 mag will provide a useful advantage.
So,do we gear up for the 5% shot?
I prefer 7 lb rifles to 9 lb rifles.I shoot better with rifles with moderate recoil.
I shoot better if I shoot more often.Ammo prices and barrel wear are factors.
Then there is the mess the extra velocity of a magnum makes at 100 yds.You will have more edible meat with a 308.
I realize,for this poll,our choices are limited.These are both good cartridges,but,if I could only have one rifle,there are others I would think about.I would not choose the 300 win mag,but the 308 would be on the list,with the 30-06,the .280 Rem,7-08,etc.