Either will / can be equally accurate.
Art mentioned many reasons for the 308's popularity. I'd agree with all of his observations.
In addition I'd add that if I had to guess where the idea that a 30-06 is inherently less accurate than a 308, if probibly comes from comparing stories of old 30-06 guns to newer 308 guns.... as much as we all miss some of the touches and features of older guns, a very good rifle has never been more affordable or easier to find from any number of makers... just a hunch.
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