Treatment of excess storage within the quota systems of Microsoft OneDrive differs substantially from DropBox.
If your Dropbox folder is over quota then file syncing will stop. Files will not be removed, and syncing will resume when you bring your account under quota again.
But it appears different with OneDrive in Microsoft's upcoming service agreement changes
"(they will) fix your account by removing excess content"
- Storage Allocation. If you have more content stored in your OneDrive account than is provided to you under the terms of your free or paid subscription service for OneDrive and you do not respond to notice from Microsoft to fix your account by removing excess content or moving to a new subscription plan with more storage, we reserve the right to close your account and delete or disable access to Your Content on OneDrive.
- Service Performance. Depending on factors such as your equipment, internet connection and Microsoft’s efforts to maintain the performance and integrity of its service, you may occasionally experience delays in uploading or syncing content on OneDrive.