Just to clarify a little further - only a SmartSync profile (that has run once already, so it has a database of 'previous-state each side' to search for possible candidates) has a chance to replicate renames/moves by renaming/moving (assuming the target system permits that). Backup & Mirror profiles can also replicate the new structure, but only by 'deleting old / re-copying new'. SmartSync profiles that have no database yet (or you Clear it), or where no potential matches are found in it, will fall back to this delete/re-copy mode automatically.
Bear in mind that if the file has been moved and edited, it will certainly fail (as the hash values won't match, so it won't be considered) so the slower method will be used
Bear in mind that if the file has been moved and edited, it will certainly fail (as the hash values won't match, so it won't be considered) so the slower method will be used