6mmBR isn't the "most accurate." It has great "ballistic performance" (i.e., low wind drift and drop) for its level of recoil. If precision rifle shooters could get it to feed reliably from a magazine, it would have prolific use.
If you go to the sticky thread, "what the pros use" you'll notice that 6.5CM, 260Rem, 243 Win and 6XC top the list. I've been reading that 6CM is starting to make inroads also. Within these chamberings there are adv/disadv that have been discussed at length. If you reload, it doesn't really matter what you go with.
Do not confuse "ballistic performance" for accuracy. Accuracy is being able to hit the target you're aiming at. Hitting the same point repeatedly is precision.
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If you want good ballistic performance, the tradeoffs are usually high recoil or short barrel life. The cartridges above (e.g., 6.5 CM) provide acceptable barrel life (better than 6mm) and moderate to low recoil for great ballistic performance.
308 Win, for example, gives you great barrel life, has a tremendous selection of match grade ammo and reloading data available, moderate recoil, but is on the lower end of the ballistic performance spectrum.