One can get winded running up two flights of steps, takes only a few seconds and you are winded but your not burning many calories.

1 hour of steady walking should burn more calories than the 20 minute bike. Running is the same way, still about 90 calories a mile, you just get there faster. I really think think though that you can narrow that gap by riding as hard as you can or doing intervals on the route. But, you can soft pedal, or catch a break from a downhill while riding and not get as much benefit.

If your intention is to burn as many calories as possible in the shortest time, running is better than biking (IMHO), up to a point. The exception is when going for a long and fast bike ride, trying to maintain over 20mph. The more wind resistance you make by going faster and faster really makes you work hard and calories burn. And big climbs burn calories. So despite not being able to burn the same amount of calories per mile, what's nice about biking is that you can rest here and there and sustain a longer workout than running/walking. I look more at time than miles. In 1:46, I can run 13.1 miles and burn an estimated 2000 calories. On the bike doing 31 miles, I burn an estimated 1600 calories for the same amount of time. Ask me to run another 13 miles, I will hate you and suffer greatly and may not finish. Ask me to ride another 31 miles on the bike, no problem. So while running is more effective, most people cannot do it as long and therefore do not burn as many calories.

Wow, rope jumping.... http://www.mayoclinic.com/health/exercise/SM00109