Well, a few major differences I'm seeing at a glance:
- X3DOM supports Flash as well as an X3D plugin. A-Frame is specifically targeting WebGL and has a much smaller surface area
- A-Frame is based on ThreeJS rather than a custom engine
- A-Frame seems to be embracing modularity a lot more than X3DOM, and it seems likely that users will be able to build highly specialized components published as npm modules (much like we see with React components)
- A-Frame is specifically focused on VR out of the box
- The markup language and intended target audience is significantly different