Nice thing is that the desktop app can sync/save copies locally and does private backups, but you can also save/sync and store data in OneDrive, private server, or corporate internet via a samaba share (Free version only syncs to OneDrive, but IIRC does local backup in desktop app).
Architecturally it's a very impressive product and makes some pretty creative uses of the windows folder hierarchy to get it's job done.
I think OneNote was built with a crashfirst mentality - It is very hard to lose data w/ it. Their QA team is damn impressive too, I've been a follower of theirs for a while.
My only complaint is the lack of true real-time sharing ala google docs's Operational Transform (they didn't exist when it was made), but it does come close. Opening a shared notebook in class and having everyone collaborate on the note was an awesome experience.
It's inking support blows everything out of the water IMHO. It also has a lot of the advanced automation features you can access by integrating OneTastic.
Only real issue I've ran into is that it gets to be a pain to print with as it has some wonky scaling features and the page layout feels like an after thought.
It is also hard to get groups of people to use it effectively because it is basically a WIKI and needs to have the same kind of discipline / habits to make it usable.
If they can do inking support with Operational Transforms, they may be able to have a replay feature without even trying - something that many teachers seem to really want out of the product.
My friend and I love the product so much we've been trying to make our own online version with inking support w/ paper.js share.js, github, and localstorage.