I am interested in opinions, theories, and facts about the relative advantages of a slotted headstock over a solid one (or vice-versa).

There are two advantages of ths slotted that I can think of.

First the ends of the strings are safely tucked in the slots and can't puncture you or the lining of your gig-bag.

Second, the strings being on rollers get pulled down more steeply against the nut. This should give more force in the direction perpendicular to the length of the string.

I prefer the looks of a slotted head, but that is subjective.

Murray