I don't think any ONE product can be used solely within an org, but we do a good enough job I feel. We needed a solution that was user-friendly, easy to navigate and use from a permissions standpoint. As a growing org, we desperately needed something to house all of our files instead of relying on everyone keeping multiple copies on computers. Our biggest problem OneDrive helped with is ONE location for all updated marketing materials and projects we are working on.
There are a few people that are using GDrive or Box, etc. but the move to OneDrive was seamless and easy for us to make happen and was done quickly and with relatively low effort.