It really depends on what you want to use it for? Any chambering can be accurate if it is loaded right to compliment the rifle it is shot out of. Are you talking knock down power, long range stuff, a flat trajectory, what exactly? It also has a lot to do with bullet type and weight.

Technically for long distance stuff a heavier longer bullet works better because it has a better Ballistics Coeficient, and the weight helps in the wind. This why many Military long distance match shooters and snypers like the .308 so much, and tend to go with heavier bullet weights at longer distances (1000 meters). Sure it's not as flat, but it has a better BC and carries more energy to the target.

As far as flat shooting and accurate most of the varmint type cartridges work really well, like the .223, .220 swift and 22-250 and the likes.

For utmost accuracy it really boils down to the guy loading the rounds and how much home work he puts into it.

I used to have a browning HI Power I bought used from a coworker in the military. He gave me a bunch of handloads he had left for it when I bought it. It shot pretty good with the right factory ammo, but was amazingly accurate with the handloads he worked up for it.

Paul