I'm kind of a 6mm freak to begin with so this question may be right up my alley
I started with a standard 243win, got bored with that & rechambered to 243AI. I shot that round 'tl the bbl gave up the ghost & was really happy with it. I can't take anything from the 243AI.
I rebarreled that rifle to 6mmAI which is IMHO, a step up in pretty much every category from the 243AI. I'm still shooting that particular rifle/chamber with 85grn bullets. the 6mmAI should get you 3600 or better with 87grainers in a 26"bbl & acceptable chamber pressures.
My favorite 6mm hands down is the 6-284. I built mine on a 700 long action, McM A-5 stock & 28" Kreiger Barrel. I'm running the tried & true 107SMK with Ramshot Magnum at over 3400fps with room to spare. The 6-284 offers some a advantages (noted above I think). The first is LAPUA brass which I think, speaks for itself. The second is '06 powder capacity in a shorter OAL than the '06, you will have more room to fiddle with seating depth & chase lands. Forming cases is so easy "A caveman can do it"
, simply neck down Lapua 6.5-284 brass & voila! You have new 6-284 brass.
Second choice is 6mmAI hands down. Longer neck, very close velocity wise, pretty easy to form cases & VERY accurate.