I've had 3 coats over the decades....love 'em
My personal observation is...coats drop less fur on an average....but when they blow their coats....it's an event. I believe with coats...the outer longer guard hairs hold much of the undercoat as they shed and therefore less day to day shedding....but brushing your GSD will become a regular event. Coats are softer as well, I do believe.
Matting might be more of a problem with coats if you neglect your grooming responsibilities...
Feeding a raw diet does make a difference in coat and daily shedding I believe...my first two were kibble dogs...current is raw fed and there is a very noticeable difference in shedding.
For me, coats were a preference in aesthetics..not huge but enough to make a choice.