The rider (you must have seen that coming )

But seriously, I think it depends on who you are. A heavier person needs the wheel to be stiff more so than a light person. I can climb on pretty flimsy wheels because I'm 150 lb and don't put out a heck of a lot of wattage, although even I have my limits. Rubbing the brake when out of the saddle is a bad thing for anyone. When I was 120 lb every wheel felt stiff.