Shay was the original geared loco, at least the first commercially successful design. The Climax design was supposedly the most flexible and followed rough track the best, but was fairly complex mechanically. Heisler was the third design and was generally the fastest for speed, and mechanically simple, with the crankshaft directly attached to the drive shafts, instead of additional gearing like the Climax needed. Only 2 axles were gear driven, with the other 2 driven by simpler side rods.
Numbers sold reflected not only the order of development, but also probably what the woods crews were already familiar with, as well as parts supplies, etc. As I am more familiar with the Heisler, I prefer it to the other two makes but also I think it is overall the better design for all around use. As ours is 99 years old this summer and is still giving good service with minimal major problems, that has to count for something!