Well..I've killed about 150 with a .243...And at 51...I ain't a kid anymore...Dropping a deer in its tracks with any centerfire isn't a problem...Just put a bullet through the shoulder blade...Stay away from a .260 unless you handload...It won't do anything to a whitetail that a .243 won't do.

If you do want to go larger than a .243, the 7mm-08 is a good round, as is the .270...But, they are very close to your .308 in performance...Any deer hunter could chose any of these 3, and several more and hunt with their entire lifetime and never blame the cartridge for loosing a deer...

The .243 does give you a larger gap between the others and your .308...And it also can do double duty on crows, groundhogs, coyotes, etc...