You may well have a challenge. While calling:
MyDbContext.Database.CompatibleWithModel(throwIfNoMetadata)
in EF5 looks like it would provide you with the information, the EF V6 version of the documentation includes this note:
If the context was created using either the Model First or Database First approach then the model is assumed to be compatible with the database and this method returns true
I cannot recall any of the EF6 change logs indicating a change in this area (this does not mean there wasn't one), so it is not clear whether this is better documentation or a real behaviour change.
Some debugging with the EF source is probably necessary: however EF was only made open source after V5 was released.
EDIT: Additional. Looking at the first version of System.Data.Entity.Database
its XML doc comment include the above quote.