I bulit the LURCR in .308, but I also have several hunting rifles in 30-06.
Rich wanted a .308 LURCR, so that is how it got done.
My "Hog Hammer" is a vintage 1938 model 70 in 30-06.
The .308 has slightly better inherent accuracy as a round design than the 30-06, but it leaves the barrel about 150-200 FPS slower. They use esentially the same bullets.
The .308 allows for a slightly shorter action, which can lighten a rifle up a bit.
The 30-06 has more knockdown power available, but can be loaded down to .308 specs if so desired.
Ammo availability for both of them is easy, but currently there is more surplus .308 on the market than 30-06. This allows cheap shooting for practice.
I find both of them easy to load for, and have Dillon dies for my RL550B for both to load practice or hunting ammo.
For best accuracy match type loads, I still use the single stage press, and a Redding powder measure.
The .308 is slightly more economical, as it uses slightly less powder. There is very little difference in perceived recoil, as the .308s are generealy lighter than the 30-06s. The net result is that felt recoil is about the same in bolt guns of suitable action size shooting similar loads.
I love them both, and would be hard pressed to make a permanent choice of only one of them. If anything, I probably lean slightly in favor of the 30-06, as I have more rifles in that caliber. I favor bolt guns, and the difference in weight between a full length 30-06 action and a shorter .308 action is not large. Hence, when hunting with the 30-06 I have plenty of accuracy, a bit more power than with the .308.
If I had to run up hill and down dale a lot, I would probably go with the .308, as I am getting lazier these days, and every ounce is starting to count more and more.