Registered user upload/downloads – Joomla or WP?

Trying to decide wether to use WordPress or Joomla.

I need the ability for users to register with the site enabling them to login to their own private area where they can upload and download files which only they and the site admin (me) can access.

• They won’t be adding posts or editing pages.
• Each user can only access their own files.
• It would be good for them to have a “profile” which they can update/edit simple information such as their contact info.

Is this possible with WordPress. Maybe there’s a plugin? Any suggestions appreciated.