Recently we faced the problem of not able to pull data that is present in Windows Authenticated Web Application from a Claims Based Web Application. These two web apps are on same server.
Tried all possible ways like LINQ to SharePoint, Client Object Model, 2007 lists.asmx etc. but no luck
Finally, we have added a registry key called "DisableLoopBackCheck" and set its value to 1.
More information on this can be found here