The K31 is an absolute beast of a surplus rifle, especially when shot with GP-11 (which it was designed for). I was blown away to see just how accurate the elevation adjustment was on the rifle.
Back to your somewhat original question, 7.55x55 swiss is VERY similar to .308.
TBH, though, an out of the box Remington 700sps tactical in .308 would probably beat it. Those are killer out-of-the-box shooters too, and they aren't overly exotic (widely available, not ridiculously priced, chambered in .308 and .223).
One thing no one has mentioned and contributes to their accuracy is the trigger. All of my K31's have amazing triggers, ESPECIALLY if you consider they are battle rifles. There's been a couple of times I've lit one off before I was ready because the trigger break is so smooth and crisp. They are infinitely better than any other milsurp I've handled and considerably better than factory triggers on most modern rifles.