Ntfs quick, as the name implies, is faster in performance than just the Ntfs. However, Ntfs seems to do better work than the Ntfs quick, as the Ntfs operate by just deleting files and not check the disks as it feels it is not needed. That is the way it is designed to function, though. However, Ntfs does a routine work by checking the disks and also deleting all the files.
These are done while trying to format an operating system. Due to the way they function, they are thereby advised to be used for a particular function that best fits them. It is advised, and as usually done, to use the Ntfs for a fresh or new drive. Nevertheless, you can use Ntfs quick for a drive that has just been recently formatted. So, if a driver had not been formatted at all, or for a long time, Ntfs is recommended to be used. However, if a drive has just been formatted recently using Ntfs, then Ntfs quick can be used to do the formatting.