The 155 AMAX is loaded by Hornady in their .308 TAP load, and this load has been extensively tested in gelatin by various agencies. It's performance in humans and deer is expected to be very very good, and it is highly recommended in .308 and 30-06.
The basic bullet design is a thin jacket, a soft lead core, a plastic tip, and excellent uniformity. As in the old days, penetration will be governed mostly by sectional density and impact velocity. If you need 12-15" of penetration for human or deer sized targets, keeping the impact velocity below 2900 ft/s is recommended for AMAX bullets of moderate sectional density (155-168 AMAX in .308). Once you get to the heaviest AMAX bullets in a given caliber (140 grain 6.5 and 208 in .308), keeping the impact velocity below 2900 ft/s will give you more like 18+" of penetration, and the issue becomes whether or not the bullet weight and impact velocity provide sufficient energy to accomplish the task at hand.
There are no magic bullets, but the high BCs and accuracy of the Hornady AMAX line tend to deliver long range performance if the sectional density and retained energy and velocity are chosen properly for the task.
I wouldn't batt an eyelash if I needed to use any AMAX above 5.56 mm in a non magnum load on deer.
Thank you again for this valuable information! My impact velocities will definitely be within the limits of the A-MAXs and should work exceptionally well. To me these things are pretty much the magic bullet, high BC, available in great weights, match grade accuracy and tolerances, and wicked performance on game. I can't wait to try the 208s in my .308 Norma and the 168s in my cousin's .308 Winchester!