Which burns more calories? Cardio or calisthenics?

Depends how much effort you put into the calisthenics and how fast your jog is.
So the answer is no, yes or maybe.

As a rule of thumb cardio burns far more than strength training but you only get out what you put in.

Look up your activity here and compare the METS....
prevention.sph.sc.edu/tools/docs/documents_compendium.pdf