Firefox

I've been using https://github.com/mbnuqw/sidebery
It also suggests you a way to hide the top bar, it can be dynamic or permanent depending on how you configure your userChrome.css

It provides you a way set up snapshots, although I haven't tested the restore functionality hehe.
I'm not sure how you can export them and back them up.

The one I know works for restoring your tabs is https://github.com/sienori/Tab-Session-Manager
But if you use sidebery to have your trees, panels, and groups, this one won't restore them, you'll get back on long list of tabs in a single panel, with no groups or trees. I already had to restore a session with this one because I changed computer. It has a way to backup your sessions in the cloud.