no such thing as too much gun, as long as you don't go to extremes. 300 win mag is fine.
however... i suggest you pick the rifle first, then do caliber.
308 and 300 win mag have a lot of overlap, and really, are not a similiar comparison. so, go find a rifle you like the feel and weight of, then account for everything else.
i've used about everything from 25-06 on up thru 338 win mag for mulies and whitetails. in my experience, the most efficient killers are 7mm's - 7 rem mag, 7-08, 7 rum, 280, etc etc. that said, the cartridge wasn't the over-riding reason for picking a particular cartridge - it was the rifle platform. in thick-n'-nasty, i want a very short, quick gun. in very open country, i want a hard hitting, light-to-moderate weight gun. in river breaks, i demand a very light gun...
anyway, look at the platform first - most any cartridge from 257 roberts up to 338 win mag work well on deer, and there really aren't any bad choices. once you decide on the platform, by default you would've decided on the action length. then it is just a matter of picking a cartridge that fits that action length... a 308 win (short action) and a 300 win mag (long action) are worlds apart in feel, but close enough ballistically for under 300 yards shooting that it is the rifle, not the cartridge, that makes the difference.