I have always been curious if there's any difference on the safety records between the A320 family and its only competition, the Boeing 737 family (the Classic). I wonder if the introduction of full flight envelope protection system with fly-by-wire in A320 series potentially could have resulted in lower accident rates.

It turns out to be that Boeing has a handy/nice stats doc summarizing the data: http://www.boeing.com/resources/boeingdotcom/company/about_bca/pdf/statsum.pdf

Quickly reviewing, the 737 Classic has a higher hull loss accident rate (about 2x of A320 series), but the 737 Next Gen series has a lower rate. From a cursory search, not enough data to conclude that there's any statistically significant differences.

What's notable is the higher accident rate (about an order of magnitude) for DC 11, which is primarily used for cargo operations nowadays. Considering what McDonnell Douglas did with the DC 10 cargo door issue (to save cost, they knowingly ignored critical problems that could be (and actually resulted to be) fatal), it's not a surprise. By the way, the FAA has a summary on the tragic accident and an animation on how the cargo door failed.

Thanks to safety regulations and engineers, the overall accident rate has been steadily decreasing.