alter database backup controlfile vs cp Linux file
If you just move/rename control files (cp, mv ...) and modify accordingly control_files parameter - no need to do any recovery.

You may use cp only when instance is down or in nomount state. 
Otherwise, you can get inconsistent control file.
If we do:   

  ALTER DATABASE BACKUP CONTROLFILE...


then we make "old", "not current" controlfile - backup controlfile.
With cp we make "current" copy of controlfile.

If we have current controlfile - no recovery is needed.
When controlfile is a backup controlfile then it requires recover and open resetlogs.

Here's a link to documentation -- old, but explains the concepts well.