Most likely, the entity container name in your two EDMX files is the identical. You must alter one of them, if not both.
To access Model Browser, launch the GUI designer. Look for a node that says "EntityContainer: Entities". Toggle it. Change the properties.
to another object. Restore and construct.
Taking advantage of this, since it is the first result on Google for the error message.
I once came into this issue because the assembly containing the model/context was changed and a copy with the old name remained in the application's bin directory, just in case anybody else runs into it while only using a single model/context. The old assembly file needed to be deleted as a fix.