Stats Maintenance after Restoring to Newer SQL Server
I would recommend to Update statistics as well as compatibility level to the latest version of sql server (provided your application supports it and you have done proper full business life cycle testing). I have written about full list of steps when moving from lower version to higher version

As a side note, please don't use sp_MSforEachtable - Its not supported. There is a clever way of doing it.

Compatibility level matters - see What is the actual behavior of compatibility level 80? and Clinging to old compatibility levels form Aaron Bertrand