I looked at the American, but I already have other rifles. I too, was a .270 for yearas. I have an old Ruger M77 that I had since 1976. Later gotr a Remy 700 in the dame cal. But I too found out that I really do not need all that power. I can get by with the .243 or 7-08. Have a Rem 700 and Winch. Mod 70 in those cals. They work well without all the recoil at the ranges I usually shoot at.
The .308 is good as is the .30-06. I like the .308 length cartridges like the .243 and 7-08 cause the rifles are a bit shorter too. The American looked good, just don't know if it is made in both long and short actions. Probably not, to cut costs. But, I really don't know. Almost bought one in .308 myself cause I don't have a gun in htat caliber. I do have a .30-06 right now in an old Remmy pump gun, Mod 760. Don't use it much cause it is much like the .270, a long action cartridge.
Performance with either is much the same. You just might get more recooil off the .30-06 in the heavier bullet weights. These days, you can get a wide range of bullet weights in factory loads. Couldn't do that in the "old days" so I reloaded the .270 and 06 down with lighter weight bullets. Really not much different than the .243 and 7-08 in recoil and performance. Now I have several of the guns in those cals. so I don't have to do that much. I just stick to the standard loads in each.
If yea get either caliber, it will work well. Just a a matter of preference. Ya also may consider ammo availability in your area. I know that the .308 is always scarce around here, but there is plenty of .30-06.
Good luck with your purchase.