Go with the 6.5 CM. Beats the venerable 308 from a ballistics perspective. It also has a regular twist rate while the 308 has a “slow” twist rate. But if the additional 0.044” in diameter (as well as a bit more energy) matters to you, get the 308.
Some folks tear apart their Tikkas right off the bat and reassemble them. Others upgrade an assortment of things right off the bat. Some do both before ever seeing how their rifle shoots.
Shoot it first before messing with it. Mine have not required any adjustments or upgrades other than getting hand-loads. All have shot amazingly well straight from the factory.
You haven’t asked but the Razor LHT and Zeiss V4 scopes are a great pairing as is the VX5HD.