Hello,
@Kozushi
Yes jumping rope is a fantastic tool if one want to look thinner, as you mentionned. Basically, it wonderful to get some muscle toning.
Contrary to running, which of course has its benefits, jumping ropes teaches you how to move your leg extremely quickly without effort. It creates some kind of flow.
Performing with a light rope may permit you to use different footwork pattern. Using an heavier one may benfit more on your shoulders, arms and grip. In both cases, core always have to be engaged. It also teaches how to get strong but relaxed shoulders.
IMO, running with heavy hands can build even stronger arm / shoulder, but still lean. Nonethless, you will work less on footwork, because it remains running.
Depending on the sport you do, footwork may be more or less important. For instance, this is crucial in boxing, MMA, etc...
As always, the best option would be to perform both jumping rope and heavy hand running.
Kind regards,
Pet'