It matters to the cow.

(Just Kidding)

I think good quality leather should last as long or longer than cheap quality plastic or rubber. Also, leather tends to be softer and more pliable than hard plastics, although the mudflap I made from an old yoga mat is very leather-like,

Leather mud flaps would nice a nice touch if your bike had a leather seat, more so if you had leather wrapped bars, and especially so if you had a whole retro/organic theme with a leather seat and leather wrapped bars, plus cork hand-grips and metal fenders.

I think the main issue is pliability so that the mudflap doesn't break, or break the fenders when encountering an obstacle.