I agree with the reply of Dr. David Turrell: going down stairs is easier than climbing up them, whether that descent is slow and steady or fast "controlled falling", as mentioned by other responders; and I also find going up stairs two at a time both easier and less dispiriting. However in contrast, when I was at college in London in the 1960s, a favorite game was racing up the "down" escalators at tube stations and down the "up" escalators. While the former was more exhausting than climbing stairs but relatively safe, the latter "controlled falling" demanded high mental concentration and was both foolhardy and highly dangerous.
Comparing the actual work done by the human (or animal) body in climbing or descending stairs to the theoretical physics notion of work as - in this case - equal to the increase or decrease in potential energy is not valid, as in climbing stairs additional energy is wasted as heat loss during the operation of muscles (why you sweat after a hard climb), while in descending the potential energy is not recovered but _must_ be dissipated by the body in resisting the force of gravity (this is where controlled falling comes in) in order to maintain a steady speed. This act of resistance requires the expenditure of additional muscle energy. If you run down stairs, only partially resisting gravity, it doesn't help, because part of your potential energy is recovered as kinetic energy and you still have to dissipate it in slowing from a run to a walk when you reach the bottom.
As for comparisons of steps and slopes, I work in construction, where Building Codes and Health & Safety legislation now demand shallow slopes for accessibility. This has led to significant changes in design, in order to accommodate extended ramps at entrances and between floors of slightly different levels. This becomes important when considering egress in case of fire, because the horizontal travel distance of the ramp is much longer than that of stairs, potentially increasing travel time.
Accessibility considerations aside, on the basis of other responses it seems that there should be a critical slope - probably highly influenced by body configuration and circumstances - below which walking up a slope is less difficult and energy-intensive than climbing stairs and above which the opposite is true. Also, when considering outdoor changes of level, the weather must be taken into consideration: in wet or icy conditions using stairs with flat steps is likely to be considerably safer than using even a shallow ramp.
