Quick Recovery searches for files and folders using file system information. It quickly scans catalog of the volumes and shows your files/folders .This is helpful in recovering data quickly when the volumes are not mounted (due to corruption).
Raw Recovery, on the other hand, is the signature-based recovery of data. In this process, the application searches for files based on specific signatures and when it gets a match, it classifies them accordingly in tree view. User can preview the data and save it at a desired location.
Raw Recovery may take more time but it is very useful in case of severe corruption.