How bad would a broken rib feel?

It can be very : Painful but pain tolerances vary from individual to individual. Even a bruised or contused rib can be quite painful to the point that breathing can hurt. If causing enough pain or breathing difficulty, see your doctor.

Hurts a lot: Since the rib moves every time you breathe, it is going to hurt a lot. Treatment is control of pain, as well as keeping you breathing well. Consider it like being punched in the chest repeatedly.

Rib fractures : Simple rib fractures are treated conservatively with pain management only. Certain rib fractures that result in breathing difficulties and / or relentless pain are treated surgically. I use titanium plates to repair the chest wall.