Up to 600 yards, the most accurate rifle I have shot is a much modified .223.
Over 600 yards, the best is a friend's full custom 6mm Remington on a Tikka action. History has bypassed the 6mm Rem in favor of the .243 Win and a whole host of 6, 6.5, and 7mm factory and wildcat rounds, but that does not mean it is not a good performer.
But the true (and unsatisfying) answer is "whichever reasonably suitable caliber you have the best barrel and ammunition for."
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