WordPress for project management and collaboration

Clogged inboxes are a problem many of us have.  I still live in fear of missing something important because it got buried to page 2 of my inbox.  Gmail helps a little with threaded conversations.  If a project is generating a lot of messages, I'll divert them to a dedicated folder so it won't flood my main inbox.  But these all seem like band-aid fixes, not lasting solutions.

I've got a little experience with Basecamp from a class I took on project management.  Having a dedicated space for work-related communications would be a huge step up.

Until now, I was unaware that WordPress could have collaboration capability.  I happened to be watching an interview of WordPress founder Matt Mullenweg, when he mentioned that his company Automattic had completely replaced e-mail by using the P2 theme. It has a very Twitter-like feel, from looking at this demo video:

Another recent development is the CollabPress plugin.  This one seems more like a Basecamp-lite clone.  The killer features are that you can assign tasks and set deadlines viewable in a calendar.  More like having a live to-do list.  Here's a video review:

The Daily Plugin: CollabPress from WPCandy on Vimeo.

Together, P2 theme and CollabPress would be a great combination.  How do you guys think it compares to Basecamp or similar apps? 

Going on a tangent, I wonder if having company-wide employee transparency would spur productivity?  Like if you had P2 theme or CollabPress feeds viewable by the whole office.  People would feel peer pressure to write about how they're doing their jobs and taking care of business.  If you missed a deadline, everyone would know it.  Sharing and communication would be more convenient.

What project apps do you use?  Any recommendations?