From the Store description, we have a changelog for the new v4.4:
- Improved design
- OneDrive for Business support
- Sign in with both your personal OneDrive and your OneDrive for Business accounts
- Organize and open your OneDrive for Business files
- Save new files to your OneDrive for Business account
- Easily send your OneDrive for Business files
- Bug fixes and performance improvements
While you can only have a single OneDrive consumer account associated with the OneDrive application, you can now use multiple 'OneDrive for Business' accounts. You can switch between any configured accounts just as in the Android app, using the new pane that pops up from the left. Unlike on Android, where you can swipe the pane in, here it's triggered by a tap on the menu icon, top left in the UI:
Confusingly, the two main panorama panes are the same as the two main extra options in the pop-up menu pane. But we'll cut Microsoft some slack here, it's trying to make a single application look the same on multiple operating systems.
You can update OneDrive (it's baked into Windows Phone 8.1) in the Store client, as usual, on the phone. It's a good complement to the new Files utility for the platform, which handles local files.