A full format does not just clean the partition table data, it also checks every sector on the disk surface for corrupted ones. This is primarily why it takes so much longer to perform then a quick format. A quick format just rewrites the partition tables.
From a performance standpoint, there is no difference. When the HDD writes a file to the disk, it just finds the next available "free sector", and overwrites whatever is there (regardless of whether or not it is a 0 or a 1). Think of it like this: a quick format just "deletes" all of the files, whereas a full format performs a sector check of the drive surface, and depending on the formatting utility, may fill the drive with zeroes (the default format utilities included with Windows do not zero-fill the drive. Most disk manufacturers provide diagnostic utilities which include the ability to do this.
If the drive is brand new, you should be fine with a quick format. If the drive has corrupted sectors (or even if you think that it does), it would be worth your time to do the full format. If you want to play it safe, ensure that you do at least one full format to the drive. That should reveal all bad sectors, and from then on, you can just do quick formats.