No, a full format scans for bad sectors which is why it takes longer. A quick format erases the files just as well as a full format.
You can use something like this http://www.fileshredder.org/ but virtually nothing makes a file completely unrecoverable if someone is willing to pay enough money to recover it.
It's a common mistake
People think that the extra time for a full format is because it is erasing the files better but it's not.