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.

I do personality like Simple Tab Groups.

You can use Firefox bookmarks to do this. Select as many tabs as you want, right click, and you can create a bookmark folder containing all your tabs. When you want to reopen them, right click on the bookmark folder, then click "Open All Bookmarks" if you want to open all of them at once.

Tab Stash because it organizes Tabs in a tree style side menu, it's awesome