I would say Teambox is a twitter-like approach to project management. You can either refer your message to a specific conversation/task or just make a status up

I would say Teambox is a twitter-like approach to project management. You can either refer your message to a specific conversation/task or just make a status update like "Working on xy". I have used Basecamp for years, and the main difference is, that Teambox is (in my opinion) better to stay on top of conversations. I've often found myself losing track of conversations in Basecamp because of new threads being opened and older threads moving to another page.