A few more added notes...
One primary design issue with any revolver is proper axial alignment of the chamber with the forcing cone and bore. Solid frame revolvers have this licked easily, as the cylinder rotates around a central pin that is held in alignment at both ends.
With a swing-out cylinder, this gets more complicated, as the cylinder needs to be supported by a yoke or crane that is strong enough to resist bending with normal use. The cylinder pin also needs to be held in alignment, at least at the rear and preferably also at the front, using some sort of mechanism that allows the cylinder to be swung out easily. This adds mechanical complexity and cost. Different revolver makers have toyed with various different methods of accomplishing front cylinder alignment.
On a related note, most solid-frame revolvers can be reloaded by pulling the cylinder pin and removing the entire cylinder rather than using a loading gate, and a few older designs rely primarily on this method; however, there is an obvious risk of fumbling the loose parts. Most modern solid frame SA revolvers are not intended to be reloaded this way; it's possible, but not easy, and it may require tools.
The Schofield was distributed to the cavalry in small numbers (compared to the Colt S.A.A.), but lost out to the Colts because the Colts could use the shorter .45 Schofields cartridge and the Colt .45, whereas the Schofields could only use the .45 Schofield cartridge, causing logistics problems.
One interesting footnote to this story is that S&W was supposedly approached about redesigning the Model No. 3 Schofield to take the .45 Colt cartridge, but they reportedly weren't interested because they had enough outstanding orders from Imperial Russia and Imperial Japan to keep the production line running at full capacity for the foreseeable future. In other words, S&W management wasn't interested in spending money to redesign the gun in order to sell a few thousand more to the U.S. Army, when they were already selling TENS of thousands of the existing design.
IIRC during the 19th century, S&W actually sold more No. 3's than Colt sold SAA's, by about a 60% margin; it's just that the lion's share went to foreign militaries rather than to the U.S. Army and the American commercial market, so the Colt was always more commonplace stateside.