Period sources usually seem to regard the Shay as the best-made and the most comfortable of the three for the enginemen. I've read a lot of comments on Climax machines to the effect that they were utilitarian, cheaply-made, and rough-riding. Heislers seem to have been somewhere in the middle, but could run faster.
Lima was the largest company of the three and had the best support for replacement parts and such things. That'd have been an important factor.
Lot of Shays were wrecked. The side-mounted drive could supposedly bind up on curves when under load and derail the locomotive. Given the obvious popularity of the type this drawback seems not to have been any impediment to sales.