EDIT: Looks like they use Windows 8, but the Windows 8 apps will need to be modified to work on Xbox. From Engadget:
In terms of whether apps will be cross-compatible between the regular Windows Store and the storefront accessed by the new console, we're told they won't. Developers will have to do a bit of work to make a Windows app suitable for the Xbox, not least in terms of tuning their UI for Kinect or the wireless controller. But Microsoft's engineers told us that the underlying similarity between Windows 8/RT and Windows for the Xbox should make this a pretty easy feat for coders. [ Ref: http://www.engadget.com/2013/05/21/xbox-one-runs-three-opera... ]