Mountains on earth often have sharp peaks and edges to them, while mountains on the moon look smooth and kind of dull in comparison. what gives the earth’s mountains their dramatically sharp shapes?

Tectonic Activities in the plates are responsible for the sharp shape of Earth's mountain.

Explanation:

Mountains on the earth are form because of the tectonic activities. Basically FOLD MOUNTAINS are more sharp because they are young and less eroded.

Fold mountains form when two tectonic plates collide with each other, both the plates are light in weight so no plate is ready to go downward, But because of speed and density difference one plate ob duct( obduction is word used for the submergence of continental plate as subduction in case of oceanic plates.). And the plate which is under pushes the upper plate which gives extra push to the mountains formation and result as a sharp peak mountains.

EX:- Himalaya, Andes.

And No such tectonic process takes place on the moon so mountains on moon are once formed and now they are eroding.