Dropbox is a file hosting service operated by Dropbox, Inc. which uses cloud computing to enable users to store and share files and folders with others across the Internet using file synchronization. There are both free and paid services, each with varying options; the service is cross-platform, with client programs available for several different operating systems as well as a Web-based client.
On the other hand Ubuntu One is a storage application and service operated by Canonical Ltd and is installed by default in Ubuntu Linux 9.10. What sets Ubuntu One apart from the other similar service providers are additional features like the integration with other services.