There is precious little accuracy to be gained from a case shape. With todays assortment of powders, just about any case can be made to work.
What does vary a lot is chamber design. If you had the same shoulder to leade parameters as a 6BR and plopped that on a case from the BR through to the 6-06, they would all shoot very similarly (this assumes you can find a quality powder to work). The larger the case, the faster you will ultimately go. Also, the faster you will burn out your throat although new additives to powders might just change all of that.
Personally, I like the 243 case because brass is everywhere or can easily be made. Most factory cases will also handle alot of pressure without blowing out the primer pockets. Dies are also readily available.
For match shooting, I want the smallest case volume that will get the desired bullets to useable velocities. The 6Rem is a bit too big. In fact, the 243 is arguably too big as well although that is changing with heavy new bullets.
The 243AI has one strong advantage in that the cases will stretch less due to reduced body taper and sharp shoulder. The increase case capacity is likely unwarranted in a long barreled match rifle. For varminting. why not.
If you look at the 22/250 derived 6mm cases like the 6XC, and 6-6.5X47L (think a shortened 243AI), we find a near ideal case volume for bullets we currently can shoot with present powders. If someone comes up with a heavier bullet with higher BC, then the 243 will become the best choice.
For point blank shooting, the PPC pretty much rules the roost due in large part to being the ideal case volume to balance bullet weight and powder burn rates. The 6BR and all its various children are doing exceptionally well with heavier bullets better suited to distance shooting.
However, when winds start to blow, there is a distinct ADVANTAGE to larger bore heavier bullets simply due to the higher real world BC. 6.5 is well established and the 7mm is coming on strong.
Something else to think about.
Jerry