I agree with UmmLila. Styling a draped one will be totally different from styling the tailored version. For me, the tailored is a piece of cake -- you throw it on just like a jacket over whatever -- skinnies or straights, crops, flares, A-line, pencil or tube skirts, culottes, sheath dress, shift, shirtdress. It works with a sleeved on sleeveless under layer. You can go low contrast or higher contrast, frilly or soft or crisp for the under layer. Shirts, blouses, pullovers, tees, silk tees -- even a moto jacket underneath. (I tried it; it worked.) You can dress it up with a luxe dress beneath, or dress it down with distressed denim and boots. It's a classic.
Drape is a mystery to me; I can't seem to wear it, let alone style it. (Not that I don't like it; I like it a lot on others. It just looks silly on me.) But I would assume you'd keep the under layers relatively simple and low key to highlight the drape feature.
