If you find the 7mm-08 "snappy" them you better not think about getting a more potent caliber, at least in the Tikka lite.
IMHO the Tikka is a great gun for 243-270 & 308. When you start talking calibers that have more recoil they are too light unless an experienced rifleshooter and recoil is not an issue. You'd be better served going to a heavier rifle.