The only difference between a Quick and a Full format is that during the Full format, the drive scans for and reallocates bad sectors.
http://support.microsoft.com/kb/302686
Now then, any modern hard drive does this automatically through the SMART process and this shows up in the Reallocated Sector Count (RSC) of the SMART data.
http://en.wikipedia.org/wiki/Self-Monitoring,_Analysis,_and_Reporting_Technology
With this SMART in mind, if you are starting from scratch with a fresh install, your drive will try to write to a bad sector, find it doesn't work and write it elsewhere and increase the RSC by 1. If this goes over a warning threshold, then Windows may try to warn you. The difficult bit is that this warning is rarely consistent.
The bottom line is that there is little reason to do a full format these days for new installs, unless you have reason to believe the drive has a problem. In which case, why are you installing windows on it and not scanning it more thoroughly?
In fact, a good thorough drive scan tool that reports SMART data like Spinrite should be all you ever need if you suspect a drive to be faulty.
Slightly less than 50% of hard drive failures can be picked up with the SMART data, but some times Windows does not pick up on such faults and tell you about them in time
What is apparent though is that in a commerical environment, 70% of drives with scan errors fail completely within the next 8 months! These drives are in temperature controlled data centres and run 24/7, but the data from Google is difficult to ignore. If you have a drive that is developing errors or "losing" files all of a sudden, it is best to get everything needed of of it ASAP!
More here:
http://research.google.com/archive/disk_failures.pdf