Deer don't require either to be knocked down. Anything 1/4 bore (.257cal) up will work just fine.
Big difference between the 2 you mentioned and seeing you said deer only I really don't see the need for a 300wm! While it is flatter/faster also comes with a price for this performance in more recoil, muzzle blast and cost to shoot.So of the 2 mentioned I'd say the 308 win if deer only is the application. If you may hunt elk or moose then the 300wm has merit.
For what you've mentioned deer/flat/fast may I suggest you considerthe.277 cal(270 win or 270 wsm). Still considered one of the best deer calibers ever invented. For that matter one of the more underratted is the 25-06, a very lethal varmit/deer cartridge that will take game further then most shooter will ever consider shooting it. Just my 2 pennys worth.
Best of Luck