Of the three major types. the Heisler should be the quietest as all the gears are enclosed, one reason it was preferred for mining railroads.
Shays had all their gears exposed and should be the noisiest. The Climax was in between but had a reputation as a slow, cruder design
which could just mean less refined, aka noisy at the same track speed. Hillcrest #10, a modern 3 truck Climax was not particularly noisy in person,
but it still seemed to be slower than the other two types of 3 truck geared locos.
Driver diameter is hard to find for Climax locos, but one California RR had a 35 ton Heisler (with 36" diameter drivers) and a 35 ton Climax (with 28" diameter
drivers). The Climax final drive at the axle had to turn 29% faster to maintain the same track speed as the Heisler. That could translate
into 29% noisier.