The idea of the 8mm06 after the war, was the fact that 8x57 brass was hard to come by, and guys wanted to use their Mausers...so recut the chamber, neck up the 06 case to 8mm, and go. Most folks then did not have the money to rebarrel, so this worked. And an added benefit over the original chambering was a little more snort.
That practicallity made sence. For the generation now, going with a new barrel would indicate the 8mm06 AI, because the cartridge is a handloading proposition anyway, the added case volume adds velocity.
I have both the 8x57 and 8mm06AI. I see an increase of 5-7% in velocity gain with the AI, both cartridges loaded to max potential. If that floats your boat, go AI.
I used the 8x57 in Africa this past fall on PG, shooting wildebest, springbok, reedbok, and gemsbok. All were killed with one shot. Load was a175 grn Sierra push by 4320 at 2850 fps, cronied. The thing was like a lazer, point and shoot, dead animals. Longest shot was 300 yrds, called by the PH. Closes was 80 yrds.
IMHO, both are great cartridges, but, loaded to eaches potential, will not do anymore or less than a number of others.