The Original is a straight leg pant and the Vintage is a tapered leg pant.
I own some of both styles. Some differences I've noticed: The Vintage have tapered legs, no back pocket, a three part deeper and longer gusset in the crotch which seems to result in more fabric around the hips. The gusset on the Vintage size medium runs about 5" wide and 15" long. The Original have straight legs, one back pocket, and a one piece gusset in the crotch. The gusset on the Original size medium is about 3.5" wide and 9.5" long.