These two barns were very close together. You find this all over the country (world): each micro-locale will have its own style barn. The farmers/builders would look around at standing barns, "Say that looks pretty good…"
With a gambrel, you take a gable roof and pop it up in the middle, creating more headroom (hay room).
A nice touch with the red barn is the dormer roof following the slant of the top slope. Also the arrow-straight eaves, no sags: good foundation. The ridge vents on the white barn also nice.
If you focus on a barn, you can feel the builder. A brotherhood, sure enough.