The main difference being that instant.page respects users' data allowances by prefetching only resources that it thinks the user intends to load. You could combine it with H2 push and/or prefetch response headers to improve the load times even more :)

It probably respects their data allowances even less, considering it completely re-fetches the page every time you hover over the link.

The difference between the HTTP/2.0 and instant.page is that the preload initiative is on the client, and not the server. I guess you could use both. HTTP/2.0 for linked resources and instant.page to preload based on the user's behavior.

Would you push everything? Or just hovered links?

In all honesty, personally I'd push all adjacent page content. HTML compresses very well, its minor compared to JS and page images. If the user proceeds to a pushed page, they'd just be waiting for the browser to do the render and collect images. It'd be a compromise, since most images are probably going to be standard page furniture, so likely cached already.