Have three barrels in 30-06 AI. A Precision rifle and two hunting rifles. The main benefit you will gain is brass stability. Performance will be on par with the 06 in normal loadings, however you can experiment and gain 50-100 fps depending on your barrel/bullet combo with normal pressures. If you hot load then you can well exceed the gains but at the risk of short brass life, popping primers, primer pocket expansion leading to bolt face wear and potential long term metal failures. If you are looking to make a magnum out of your 06, then consider a 300wm. For cool factor, just do it and you will not be disappointed.
Velocity gains will be best with longer barrels as such consider 24" barrel as a minimum for heavy bullets. However, I have one on a 22" sporter barrel and performance is as noted with 150s. I really like not having to manage brass once ackleyized. And you can keep costs to minimums by using a Lee collet die for sizing, 308 seater die for bullet seating, and from time to time FL using a standard 30-06 die to bump the shoulder back when cases get harder to extract (better to use a body die). The key when fire forming is to leave a false shoulder by running the brass first through a 338 or 8mm expander ball and then FL sizing back in small increments so there is a crush fit when chambering brass. I had a 338 WM die on hand so used that. This will minimize case stretch and reduce the chance for case head separation. not a big deal, just a few extra steps. If your smith correctly cuts the chamber you will not need to manage the false shoulder method so much. New brass requires some attention as it is usually undersize and will likely need a false shoulder. And if chamber is cut long then the described method is a safe bet.
Enjoy. My 2c.