Personally with either of those chamberings I would go no less than 22" and honestly to get the most from them 26" or longer especially with the 6-06 being an overbore. That being said, you could make an 18-20" barrel work with the 243AI but at how much of a velocity sacrifice I don't know for sure. With the 115 DTAC as your bullet choice and the slower powders needed for that combo it may not be as ideally flat as you would want.

Now all that said, there are a lot of guys shooting those and even worse overbores in things like the xp100, T/C Encore, and Savage Striker pistols and are totally happy with their performance. If I were going with a shorty out of 243AI or the 6-06, I would go 243AI with no less than 19" length just to try to keep as much benefit as possible.

If you decide you can accept a longer barrel like 24"+ then by all means go 6-06 or even 6-06AI and send that 115 screaming down range. I built my 6-WSM just for launching the 105 A-Max as fast as possible, but I went with a 28" bull barrel to get as much as I can from it. I am also getting ready to order up a 6-06AI (to replace the 6-06 I just traded away) and it will likely be at least a 26" barrel.

After building my 450BM with a 16 1/2" barrel and my 250AI with a 16 1/2" barrel I am finding a new found love for the shortys, but when I wanna go AT&T on my target (AT&T = "Reach out and touch someone" ) Then I am going to grab one of my long barrels. JMHO of course, and personal preference varies between us all.