Fast breath or upper chest is anxiety and stress and ignites the flight or fight response of the sympathetic nervous system. This over time creates disease in the body.
Slow deep breath promotes health and longevity as it works with the parasympathetic nervous system to rest and relax. Slow breath on the exhale also stimulates the vagus nerve, the largest  in the body, to help regulate hormones, sleep, digestion, and overall vitality. The overall heart rate is decreased by regulating the oxygen level and releasing  c02  on the exhale

The breath is also a gateway to higher levels of consciousness and frees the mind of ego demands. In yoga the breath works with the nadis, which are vital energy currents, to open  the life force  to major centers of the body in order to balance  the body mind and spirit. Example in the animal world: a mouse lives 28 days with a rapid heart rate, whereas a turtle lives for more than a hundred years with very slow breath.

Example of one breathing pattern that can be practiced
(breath count 4-7-8) inhale for 4, visualize how energy flows through the body, then hold the breath for 7 counts-and then exhale for 8, now visualize all tension dissolving and then rest in the pause, learn to enjoy the pause. Repeat for 5 minutes …. If one finds this difficult, begin with 1-2 minutes

Ideally practice this sequence  for 5 minutes working up to 15
Minutes per day. You will see major changes in all areas of life.