I can't honestly compare the two since I have three of the round butts. I just like the looks better. The square butt may have a slightly better grip to hold onto, though they seem bulky compared to the round. Just a matter of preference to me.
I have a model 10-8, a model 28-2, 686-1, and a 547 with 4" barrel and square butt. I also have a 3" barrel 65-3 and a 2 1/2" barrel 66-2 with round butts. To me I find no appreciable difference when shooting them. The only difference I find is the round butts are slightly easier to conceal. I have also carried each concealed except for the 547 and have had no real problems concealing either square or round butt. It is simply what you get used to.
To me, a square butt allows me to get a better grip than a round butt gun. I've actually converted my round butt 686 to a square butt with a set of conversion grips.
IMHO round butt revolvers are aesthetic abominations. I know they are supposed to be "ergonomic," which is somewhat subjective as not all shooters find them comfortable -- but they ARE ugly.
I like the round butt with a 2" or 3" barrel. Square butt on anything longer. The Round butt is definitely more compact and easier to conceal, while the square butt fills my hand and makes for a slightly more secure hold.
Square butt grips are usually preferred for comfort and accuracy, so much so that there are conversion grips to convert round butt revolvers to square butt profiles, at least on larger frame guns. I have some on both my Model 29 and Model 24 (and maybe others, can't remember).
My take is that the K-frame round butt grip frame is more versatile. It is more concealable in most every circumstance. And with the availability of round to square conversion stocks/grips they can be just as controllable as the square butt versions.
Personally, though I tend to shoot square butt Ks better and I prefer the way they feel in my hands, the round butts are easier to conceal if you stick with compact grips.
That said, in a way the round butt frame is more versatile, because you can always put round-to-square conversion grips on them.
Usually the RB is associated with a short barrel concealment gun. It it a tad smaller and more compact. But in the early years of the hand ejectors you might see any combination.
Here's a 6.5" K frame with a round butt.
And just to show the other extreme, a 2" model with the square butt.