Underhand is easier on my shoulders than overhand! Could you have this backwards?
No, I didn't. This is an old phrase thrown around by several strength and condition coaches (Jason Feruggia, Chad Waterbury), but now that you have sparked my interest; No, there is not much scientific background to support this claim. There are talks of different acromion types affecting the effect of the grip, but that is more reasoned in pressing, and has bigger support. Say close to neutral overhead pressses or bench presses vs. pronated or supinated grip [Even tho nobody does supinated grip pressing] presses. But when considering that the involving muscles and movements are just opposite, could it have an effect?
The other word against supinated grip comes from the fact that it puts the shoulder joint in a very disadvantaged position: To the front of your body. Instead of a proper pull-up or neutral it should wind up more on the sides. It's also claimed that supinated chins cause huge stress on the elbow joints (Given the logic used before).