If I'm not wrong, the quick verify just checks if the files are copied to the internal hard disk by checking the filename only.
The full verify should compare the actual file contents to that of the memory card to ensure that they are identical.
I'd usually skip the quick verify as I'm not comfortable (unless I really need my card urgently). I always use the Full verify. Just to be on the safe side.
But not once has it failed me. All files copied perfectly from day one til now. (about 1 yr).
Hope this helps.