i'd say riding fixed increase the amount of effort you need to give out.
look at other riders and see how often they coast along or spin up hill in a little gear. fixed doesn't allow for either of these options. pedal pedal pedal. if you see a hill you'll have to build your speed up before hitting it and then keep up the pressure for as long as you can before succumbing to the point where you stand up out of the saddle to turn the cranks.
it also improves your pedal stroke (or should do), giving you a more even power output and a smoother, less jacky/jerky cadence.
and down hills will have you using different muscles, too. just be careful of your knees.