Airport Security Question: Body Scans vs. Government Databases?

The New York Times has an article today looking at the debate over how big a violation of privacy the full body scans at airports would be. This provoked a breakfast discussion with my wife over the following question: Which is less invasive of privacy: government agents peeking at your body with millimeter wave scanners at airports or allowing the government to amass and access instantly dossiers of background information before you are allowed to board a flight? Below is an example of a millimeter wave scan.

So which would you pick? For the record, my wife and I decided scanning was the less invasive option.

See the excellent articles on airport security in the wake of the Detroit incident by my Reason colleagues Robert Poole and Jacob Sullum, here and here, respectively.