I know 3 stage can be set shorter - and potentially taller too. and 3 stage weighs more. but is there an advantage in one over the other in terms of actually using/adjusting them?

I think that (technically) they call them "1 stage" and "2 stage", specifying the number of extensions you have. I might be wrong on that, but anyway, I know what you mean!

Single-stage tripods are faster to put up (fewer knobs to adjust or legs to extend), and in theory are more stable because they have fewer joints. They don't fold down quite so small as 2-stage tripods, and there may be some differences in maximum and minimum height which may or may not bother you.

Sachter Speedlock are an exception, where there is a single leg clamp which controls 2 leg extensions at once.