I'm trying to come up with similar software schisms: vi vs emacs? GNOME vs KDE? Linux vs BSD? C vs C++? C++ vs ObjC? All of these differences sound more substantive to me.
Unfortunately, that seems to lead to a lot of acrimony between them. I wonder if a big part of it is that each side is convinced there won't be space for both in the future, and that a clear winner has to be declared - which I don't think is true at all. This town is certainly big enough for the both of them :)
As for drama within the Ember community itself, that's a little more complex. I think a big part of it is that Ember seems to have a lower barrier to entry than Angular at first glance, but certainly has its own catches and hang-ups, and running into those when you thought you had found a holy grail can be extremely frustrating.