Relying on the service to shut down gracefully and detach your database files cleanly is risky. I have often seen this result in corrupted files that can not be used elsewhere, and which fail to start up even when starting back up the source instance which corrupted them. Moving the files after detaching them poses a similar risk - if they get damaged in or after transit, what are you going to fall back to?
If you don't have a backup of the database, either approach could result in disaster, since you are left with zero copies of your database.
If you do have a backup of your database, copy that, and restore it. If the backup isn't recent enough, create a new one. This is a much safer approach because your original database is still intact. If something goes wrong with the file during transit, or there are issues trying to restore it on the destination server, you can always start over - having lost nothing but time.