Jomping Rope is a much better exercise, being very intense and the fact it works the whole body. Sprinting instead of jogging is about the same but is much harder exercise to maintain for extended periods of time.
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Well it all depends on how difficult the jump rope is. For 10 minutes of each (moderate skipping and moderate jogging) runnung wins, however i personally feel that i can do a very fast pace on the jump rope and i can do it for longer, which will obviously burn more calories if that is your objective. If you are just interested in which is overall better for your health then i am not sure. jumping can put a lot of pressure on your back, ankles and calfs and i wouldn't recommend it for un-fit people as it hurts!!
well i hope i helped :)
good luck
Depends how much effort you put in really, but i would say jogging because you can go further