I've personally never tried a 220 gr in the .308 Win (and it's been a long time since I owned a .308). I am a big fan of the 220 gr round nose in the .30-06, FWIW.
Seems to me that the .30-40 Krag with 220 gr bullets and the .303 British with 215 gr bullets (both at around 2000-2100 fps muzzle velocity) had pretty good reputations back in the day for being reliable game getters.
Winchester used to a load a 200 gr in the .308 Win with a stated muzzle velocity of 2450 fps (24" barrel). I'd bet a 308 Win could easily push a 220 gr bullet to around 2250-2300 fps.
Just my musings....
-Bob F.