The biggest difference is multiplayer, which was added in Warband. It also brought along a new faction, the Sarranids, some additions and adjustments to combat (for example kicking and using throwing weapons in melee), a new and more open strategic system (I think?), and more items and polishing. In short, I would say Warband is better in pretty much every aspect, which is natural as it is a direct descendant of the original. Of course, you could buy Mount&Blade just to support Taleworlds, but then I would rather buy a t-shirt if I were you.
Aw, beaten by Narrator.