Re: 6mm Krieger - difference .237 vs .237?
Not sure if this is why but some barrel makers will make a bore diameter for hard bullets. These bullets need much higher engraving forces to get them started into the rifling. The larger bore diameter reduces this force because the lands are not as tall and this will reduce pressures slighly with hard bullets, especially bullets such as solids or very HEAVY jacketed bullets.
Again, I am not saying this is why Krieger offers the two different bore diameters, especially in the smaller 6mm bore size but it is a consideration.
ALso, with a thin jacketed bullet, if your driving them very fast, at times the shorter lands are easier on the core to jacket bond and will allow slightly more velocity without bullet failure.
Does not sound like you will be shooting hard bullets but if your rifle has a high velocity chambering, you may want to try the larger diameter bore with the Berger bullets.
In all reality, you likely would never be able to tell the difference between the two with most chamberings and velocity ranges and I would say accuracy potential would be so close it would be very hard to prove one if more accurate then the other.