Visual Studio 2013 and up - Database Project Schema Compare File Is there any reason to save the schema compare file once you are done comparing, creating scripts or just simply updating?
Short answer, maybe. If being able to open a previously saved .scmp file makes life easier through time savings or consistency, I'd say it's worth saving.

With a schema compare window open, there is a cog wheel icon which opens the Schema Compare Options dialog. There are quite a few options under General and Object Types. Some are selected, others are not selected, by default. If you find yourself repeating compares that require changing the same default settings each time, that would be a compare worth saving. 

The compare also saves source and target. If one found that when comparing one's local machine.MyDB to Development.MyDB, one didn't want to see differences in ObjectType X, but one did want to see those differences when comparing Development.MyDB to QA.MyDB, one could save two separate compares.

A .scmp file can also be added to source control, if one found value in doing that as well.

There very well could be other advantages I'm not aware of, but that's about the extent of my limited experience with database projects so far.