I am in a district that has a big contract with Microsoft which includes OneDrive for Business as our cloud storage. I am so frustrated with OneDrive that I must say Microsoft has missed the mark so much on this product that, in my opinion, they are no where near the cloud but laying on the ground being absorbed by the world. Dropbox on the other hand has it right and Apple is on the right track (provided that everything works well in this new iOS 8 version coming out in the fall), and there are a host of others who have good products. While OneDrive is more of a comparison to Google Docs, not a very good one at that either, I will not compare Google Docs for this post as I am sticking solely to these two products.
What I want and how it works/doesn't work in
Moving files from one folder to another: Again, Dropbox gets this right. You can move files from one folder to another just as easy as you would on any PC interface. Click, drag, drop. Even in the app, they have a smooth way to do this. OneDrive requires the same interface as above to do this. No online way of moving documents (unless you go into the settings and set up a couple of security options and then it takes a half-a-dozen steps to do this) and the app is useless.
Speaking of apps: The Dropbox app allows you to upload, download (open in...), move, change names, access shared files, save to your choice of folder, and does so without a hiccup. OneDrive's app is a view only app. No moving files, no renaming, no saving to a folder of choice. The only thing you can do in the app is Open in...
Sharing files: Here, they are fairly equal when it comes to sharing a document. Get a link or send an email to share a document. The difference is in sharing a folder. Dropbox wins again. Click the link icon for a folder and get a link. For OneDrive, you have to invite people by email to have access to a folder. Why? Do people at Microsoft not share folders with anyone at conferences or public meetings or do they only share single documents?
I don't think I am asking for much. Microsoft's OneDrive does have a few things going for it that Dropbox doesn't: online document creation in Office 365 with collaboration, a full suite of services that includes email through Outlook Web Access, and a social aspect to follow documents and receive updates when changes are made. However, when I want a simple way to store and share documents with basic file property settings, I will stick to Dropbox.