This is a question I had a couple of weeks ago and though I’ve since decided on Office 365, I still have a bunch of unanswered questions because Office 365 is… complex. I’ll answer what I can.
Storage and backup, with versioning.
There are two different versions of OneDrive – the consumer version called simply “OneDrive” and the business version called “OneDrive for Business.” This is important because they are in fact completely different technologies/backend. ODfB is re-branded Sharepoint and Exchange and in fact worse than the consumer version in a number of ways, but more powerful in other ways. You need to be aware that there is a difference between the two when researching OneDrive.
While I haven’t used it much myself yet, ODfB supposedly has sync problems – some files won’t upload or sync, or will be lost or corrupted. It also doesn’t allow the granular offline/online sync options of the consumer versions: You can only set a top folder as offline or offline, not files or folders within that folder.
The ODfB client for Mac also may not be the great, though they recently released a new version. The Android/iOS version is the same for OD and ODfB and works well.
Granular file access control and logging
Though I haven’t explored this much, I believe this is the enterprise standard and as good as it gets, though with a complex and sometimes confusing interface. You can set access down to the single file level, and also share with people outside your organization.
Considerations for storing client-sensitive information there at some point.
I believe that you can switch from the cloud-based version to a self-hosted version of OneDrive if necessary.
Other services to consider that are similar (email, storage, document collaboration, security, reliability, near-zero IT support requirement)
For a self-hosted solution, there’s OwnCloud.
It’s still speculation at this point, but I believe that Office and Outlook will become really superb this year, as Microsoft launches the Windows 10 and Universal Apps, and the new email and calendar apps (Accompli/Outlook and Sunrise.) Microsoft has been getting a lot better the past year and I’m now trying to rid myself of everything Google, and have a Surface Pro and a Lumia phone.