I have both (.308 in bolt rifles, and .243 in bolt rifles and Handi's) but I think I'm biased, towards the military calibers.
If you have to choose between, getting just one of the two calibers .308 or .243, go with the the .308. IMO, military
calibers (.223 & .308) are always better as far as ammo availability, bullet weights, and price is concerned.
Datil is correct tho, if you can swing it, get both.