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.
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. .
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.