Is there a way of telling which version of Microsoft SQL Server a database backup is from without restoring it?
The database version can be found in the column: DatabaseVersion
From Jonathan Kehayias blog post here the number in this column:
[To those that want to edit this answer to include additional version numbers, that is not the intention of this answer. It was just for example and quoting the information that is from the link provided. The version number of a database can vary and may not be exact across every database based on what SP or CU is installed, or setting/feature that is being used. The version numbers are not documented by Microsoft and is just a simple reference to understand that the number increases as you move between SQL Server versions.]
If you try to run this command for a more recent database version than the one you're running it under (e.g. a 2012 DB from SSMS 2008), the database results display as INCOMPLETE
To check the build number of the instance check for columns:
Documentation can be found here (TechNet link).