In reply to stevefroud:
The question is, why are you slower? Is it
a) because you're being more cautious as you don't trust your feet not to slip
b) because you're stepping down, stopping to work out where to go next, then stepping again
c) because you're getting tired (burning quads!) and having to be more careful
Personally, I've found it mainly to be a confidence in footwear issue when I've been slow. Stiff boots with little feel are particularly bad. One or more poles make a massive difference on steep steppy terrain as you can lower yourself onto the lower level under control instead of having to remain in balance.
Top tip for walking on bare slippy rock - place your feet in corners so they can't slide anywhere. Next best is edges. The worst is in the middle of a flat bit as you never know when you're going to slip, and when you do you'll either a) pull your groin stopping the slide or b) hurt something when your foot comes to a stop or slips over an edge. 30 years of fishing on algae & seaweed-covered rocks has given me significant expertise in not falling over on slippery rock .