Well, maybe it's not that simple. There's deep and shallow square and there's deep and shallow round. Whether they're deep or shallow probably carries more weight than how square or round they are. Then again, square corners can be more likely to develop corrosion depending on how cleaning is done.
Barrels with radius bottom rifling (round bottom) are both more expensive and easier to clean. Don't know that one is necessarily more accurate than the other, but the round bottom is definitely easier to clean and to keep clean.
Pard, there have always been many theories about what kind of rifling is best, and always well be. Add to that discussion the issues of twists. :stir:
There have been many scores of different riflings over the centuries. Round bottom is just one.
Better/worse/no different? Depends on who you ask.
Square. To the best of my knowledge, over about the past half century the only round bottom barrels made, in the U.S., have been either custom or from very small production shops that could almost be called custom.
My limited understanding of this is that the round bottom grooves allow more consistent shots without frequent cleaning between a number of shots. The square bottom grooves (in theory at least) are easier for the patch to seal and, therefore (again in theory) are better for accuracy. This info comes from several barrel makers I talked with last fall. I would have to think that only a few folks can shoot as well that a square bottom grooved barrel would make a difference. I am certainly not in that category...
I have never had anything but square bottom. My custom 40 has a douglas barrel and it's square. All of the factory made rifles that I have ever seen are also. Geo. T.