I tried watch on left wrist and Band on right but it didn't look right to me. I have heard the Band and other similar devices called 'right wrist devices' with the implication being that they complement, and are worn together with, a wristwatch but I think for me to consider wearing both together the Band would have to be less bulky.
It's interesting because I had intended to use the Band as purely a fitness thing, I'd put it on before exercising. But now I've been using it I find the notifications & Cortana integration to be much more useful during the day then I had anticipated so I'm wearing the Band more frequently. The Moto 360 & new Huawei Watch have me intrigued (if only they supported WP).
I think for me a 'Band' in the style of the Montblanc e-strap might be fun!