The NTFS Quick would finish much faster compared to NTFS.The primary reason behind this is that NTFS Quick simply skips certain steps that are taken by NTFS.
Selecting NTFS would remove all files in the drive, then check sections of the drive for damages so that those areas can be avoided by the operating system.NTFS minimizes the possibility of data loss and file corruptions. NTFS Quick does not perform this check, which takes a longer time.
Formatting on NTFS Quick skips checking the disk, so is possible that some damage areas of the Disk would be used.It is advisable to use NTFS for drives that have not been formatted before, Where is very likely that no damaged area exist. NTFS is also Recommended for older drives that have been in use for a long time, but has not been checked or reformatted before. NTFS Quick is very much acceptable for drives that have been formatted with NTFS before. If you often perform disk checks,it is also recommended to choose NTFS Quick as the disk check would probably not see any new defects.
You can manually perform a disk check by running the chkdsk utility that is provided by Windows. It would take some time but at least you can leave it running and not have to wait around for it to finish.
NTFS is advised for fresh drives or for Hard Drives that have not been checked for errors.
NTFS Quick is advised for recently formatted drives or Drives that had been check for errors in the past. = (recently).