As others have said, sticking with the 308 makes the most sense if you already have stuff for it. Either cartridge will do the job on a deer just fine at normal hunting distances. The 6.5CM has no advantages inside 300m except the slightly reduced recoil, and even that is not a big difference when you compare the 140's in a 6.5CM to 150's in a 308.
Generally speaking I like the 6.5CM round, but it doesn't seem worthwhile for what you want. I shoot both, but I stuck with the 308 for my hybrid rifle (mid range target and hunting, sort of a general purpose rifle) for it's versatility, cheaper brass, longer barrel life, and availability of cheap bulk plinking ammo.