Reading this question last night compelled me to make a meeting today where our Windows Media Center MVPs learned more about Windows Home Server from Charlie Kindel and another gentleman from the team (I had to cut out and go to a feature team meeting before I could get his name -- but I'll circle back). I expect those MVPs will be able to give you additional thoughts, but here is a start.
In a nutshell...
Windows Home Server: Helping families with multiple PCs connect their digital experiences, providing a familiar and reliable way to store, access, share and automatically protect what is most important. *
Windows Media Center: Helping families enjoy the digital experiences stored on the PC from the comfort of their couch or in other rooms of the house with an intuitive and easy to use interface. **
In other words, two separate products with goals that are highly complementary to each other. Based on what little I saw today they will each benefit *immediately* once Windows Home Server ships. Longer term, I believe we will see the two product teams collaborating more -- perhaps even creating features unique to the intersection of Windows Media Center + Windows Home Server. After the presentation today I'm definitely going to replace my Windows Server 2003 box here at home with a Windows Home Server and start playing around to find the synergies and goodness.
* This came from an excellent post by Charlie: Why Doesn't Windows Home Server do foo? Go there to learn more about their vision and goals -- it's also a good post on feature development work in general.
** I made this up to kinda, sorta match up with the Windows Home Server mission statement for contrast. It's not 'official' marketing blurb -- but is a pretty good description of the Windows Media Center goal.