Jesse,
On the surface, Paul is correct. I tried rigging my computer running developer edition to see only my servers and not AGOL. I spoon fed it the WebMap json, which I had downloaded from AGOL, The error messages were too many to count. Like it or not (and I don't), WebMaps are here to stay, and WAB depends on AGOL or Portal.
That said, I create my viewer in Developer Edition and host it on my own server. Eventually I will have to rely on Portal. I don't want the phone call from Emergency Management asking why the WAB viewer won't work when the Internet is down.
CMV is an excellent viewer, but I think WAB is better designed for mobile devices at this point. It has responsive design from the ground up. Dave Spriggs and Tim McGee may disagree, but that's my story and I'm sticking to it. I'm a former CMV user and they never let me forget it.
Larry