Since you are talking about target shooting, the 308 and the 300 both fall off considerably at about 250 yards.
The 308 will use 1/2 the powder and a boat load of recoil less than the 300.
If you re-load, it will cost about 1/2 the price to shoot, allowing you to shoot twice as much on the range.
If you were going to hunt moose with it, I would suggest the 300.(not that the 308 is a worse caliber, but just for the extra punch)
Since shot placement is EVERYTHING in hunting, it really makes no difference to the moose which one kills him.(and either one will kill him with the right shot)
I re-load for both calibers and they both use the same bullet, but the brass for the 300 is much more expensive, and it uses about twice the powder, which makes it very expensive if you are talking about shooting a lot at the range.
The re-coil of both calibers will also figure in to how much range time you can shoot.