Heisler gears were entirely enclosed in a gear case, which made them less likely to get packed with snow and freeze up. As Bret pointed out though, the gear case is only a couple of inches above the rail and could high center on packed or frozen snow.
As others have pointed out above, each type had strong points and weak. The center drive shaft of the Climax and Heisler made the boiler set high on the frame and made them somewhat top heavy. It also necessitated a shallow fire box which impeded steaming with some types of fuel. The side drive line of the Shay allowed for a deep fire box and lower hung boiler but made for stiffer running gear which, as noted above, sometimes caused the wheels to lift off the rails. The Climax had sprung journals as well as bolsters, which made them very flexible and able to handle the sketchiest track. Heisler side frames rode on trunion pins allowing for greater flexibility than the stiff trucks of the Shay. The woods boss for a high mountain camp of the English Logging Co. told headquarters to keep the Shays down below and only send Climaxes and Heislers up on the mountain, probably for that reason. (Note, this is another case of a large company rostering all three types.)
The Climax had double reduction gears which, combined with the flexible running gear, allowed them to pull harder for a given weight of locomotive. The Heisler was somewhat higher geared, giving higher speed on good track but less pulling power. They compensated for this by using large over square cylinders, although this sometimes taxed the capacity of the boiler. Shays on the other hand were quite good steamers, and the three cylinders made them easier to start with a train.
So far as production figures go both Climax and Heisler were small, privately held, companies which were able to sell about everything they could produce. Lima, on the other hand, became a large corporation which had to aggressively market their product to make a profit. So, production numbers are not a good indication of which locomotive was best. It depended entirely on the situation, and on the whims of the buyer.
