I'm probably gonna be the odd man out here, I think that WASD movement is easier and more intuitive to control, and so will be more accurate for most people, but if you play a lot of RTS or MOBAs and have a lot of practice with click to move the precision of a mouse is still beyond any other control scheme that I know of, it's just more like the other commenter mentioned where a lot of the benefit comes from decoupling movement and attacking.
It's easier to be more precise when one thumb is only focused on positioning, instead of the mouse pointer being the source of movement location and attack location.