There are always pro's and cons when comparing cartridges, but at the distances you are hunting at I feel .308 does not offer much over .243 other then bullet weights, but IMHO that is a non-issue on think skinned animals like deer. I have shot large hos with a .243 and also witnessed first hand a young man drop an Oryx with one shot during a youth Oryx hunt (shot placement is key).
Yes, 243 is an excellent cartridge for whitetails, muleys, antelope and is downright devastating on coyotes. I wouldn't hunt elk with it, but thee aren't too many of them running around KY!
243 ammo is a buck or 2 a box cheaper (more for premium) then 308 and can always be found in any "out of the way mom and pop shop" should you forget your ammo at home. My local walmart always has way more 243 ammo then 308.
My M700 LSS shoots .25 MOA @100 yds with plain old Rem factory ammo 100 gr SP core lokts!
Recoil of the 243 is a bit less too...
Cartridge (Wb@MV) Rifle Weight Recoil energy Recoil velocity
243 Win. (75 at 3400) 8.5 7.2 7.4
.243 Win. (95 at 3100) 7.25 11.0 9.9
.243 Win. (100 at 2960) 7.5 8.8 8.7
.308 Win. (150 at 2800) 7.5 15.8 11.7
.308 Win. (165 at 2700) 7.5 18.1 12.5
.308 Win. (180 at 2610) 8.0 17.5 11.9
recoil table link
Hope that helps! Also, if you get a .243 and you decide you would rather have a .308 you can always find M700 take-off barrels cheap on gunbroker....