Yesterday I attended the “Building Windows Phone Mobile apps with SharePoint 2013” sesson, here are a few notes I made:

• The new Windows Mobile API in the Client Side APIs, in addition to SharePoint mobile SDK, makes it easy to extend SharePoint to Windows Phone. It includes authentication via CSOM, push notification possibilites, location, etc. It is probably best suited for extending specific parts of SharePoint to the mobile, such as administration of a list (support, helpdesk, contacts, etc.). Via the SDK you actually get a new project type for building an app against a list in SP2013. (Read more about building apps here: http://msdn.microsoft.com/en-us/library/jj163228.aspx)
• For other devices such as iPhone and Android, the best approach for building apps against SharePoint would be to use the REST API. (Read more about choosing the right API here: http://msdn.microsoft.com/en-us/library/jj164060.aspx)
• If you have the need for a mobile version of your intranet or external web site, the best choice is to use Device Channels

Here is an example of a contacts list made available through a Windows Mobile (picture source: MSDN, http://msdn.microsoft.com/en-us/library/jj163228.aspx)