My dad has always been a big fan of all things Ackley Improved so I guess that's where I get it. Between us we have five chamberings that are improved, four are AI versions (223AI, 6-06AI, 6.5-06AI, 338 Lapua AI) and one Kirby Allen 300AX which is a necked down 338 Lapua with his proprietary 35 degree shoulder.
From talking with Dave Kiff (w/PT&G) research says once you get past 37.5 degree shoulder angle it becomes counter productive with regard to flow characteristics. So maybe that's why you see so many "improved" cases with 30 and 35 degree shoulder angles. I know some folks claim the AI 40 degree causes extraction issues but I've never experienced any of those problems in any of the AI chambered rifles I have.
As for the 22-243AI vs 22-6mmAI, in an appropriate length'd barrel, I don't see how the 22-243AI could keep up. In a shorter barreled version, there may not be as much difference. BUT, brass quality would certainly favor the 22-243AI.
My dad has a 22-6mm that he really likes but he'll be the first to tell you, if he was starting all over, he'd absolutely have it chambered in 22-6mmAI.
I have to admit, if I were building a hot rod 22 cal something or other, with Lapua making 243 brass and the fact a 22-243 works so well in a SA 700 Remy, there is no doubt it would be a 22-243 Improved something or other.