Sharpshooter, perhaps our issue is with terms.
"Group" means, to me, 3 or more shots fired at one target by a human shooter.
.006" means, to me and anyone who knows mathematics as displayed commonly in the United States: "Six thousandths of an inch." (or 1/6.67 of a milimeter. A milimeter is the approximate thickness of a dime.)
Thus, the statement, as I read it, is that you're getting your Browning A-Bolt to launch three or more Ultramax (commercial reload) bullets into a single group, the outer edges of which are, after measuring, exactly.23 inches from side to side. (assuming the outer diameter of the bullet is 0.224"). Apparently, your Remington VSS turns in, even with your best handloads using a premium bullet, a miserable .25" group (which I, for one, will take every day of the week and twice on Sunday, if my rifle and I could do that well on demand with my own 700 Sendero SF). We don't know the contour of the barrel and the stock of your A-Bolt, but your claim is that it can with regularity shoot groups well under half the size of your VSS, with factory reloads. My heavens. One wonders why you bother reloading at all.
All of this has, IMHO, little to no bearing on the topic at hand: what would be the most versitle caliber for a light, handy carbine? Employed as it's meant to be used, it will never see a bench, except to sight it it. 2" @ 100m is perfectly sufficient for snap shot hunting use.
.1" groups? They're getting pretty commonplace, among better competitive benchresters. Not among sporter rifles.
Have I shot 3 shots that would go under 1/4" before? Sure. Does that mean that the rifle, load, and I can do it on demand? heck no.