I was just pondering this myself hence why I found this post!
I would be interested to know why I might choose one over the other, my understanding isn’t enough to position the the two implementations in my head.
Is anyone able to summarise how these two fit into the WP ecosystem?
I guess the WP JSON approach has the advantage that other users of any developed app would not be forced to use Jetpack. It can also be extended to provide routes for eg BuddyPress etc (but these will have to be installed as separate plugins).
The JetPack solution ties into WordPress.com so not sure if that affors additional benefit in terms of authentication etc.