Microsoft has some advantages with OneDrive, beyond the way Office builds it in to the way you work with documents. Cloud services mustn't mess with your stuff; you have to be able to put any file there and get it back unchanged when you need it. Google Drive tries to push you into using Google Docs by converting Office documents to its format, which can lead to a nasty surprise. OneDrive doesn't do that – it even has a recycle bin that keeps deleted files for up to 90 days.
OneDrive needs far more of the features of a file explorer in the browser, and it needs first class file manipulation tools, online and off.
In the browser, you need the features that have been in Explorer for years, like being able to pin folders for past access, or being able to quickly find all the files you edited on a specific day as easily as you can find all the photos you took in one location. Currently, you can't even jump from a document in the list of recent files to the folder that contains the file, so you can get at the related files you keep there.
Microsoft also needs a much more sophisticated sync system than making you pick entire folders to sync and ignoring all of the others unless you go to the website. The new OneDrive mobile client for Android lets you pick individual files you want to save offline, and Microsoft says that will come to iOS and Windows Phone, and hopefully Windows as well. But that's only ever going to be a fraction of your files in the cloud.
Tablets and smartphones with a limited amount of storage make cloud storage unavoidable, and Microsoft urgently needs to replace the placeholders that let you work with all your OneDrive files in Windows 8.1, synced or not. Because those placeholder files take up space and confuse some apps, Microsoft removed them in Windows 10 and hasn't yet come up with a replacement.
Persuading more apps and services to connect directly to OneDrive is key, but Microsoft also needs to work on better tools, so that you want all of your tools to put your files there.