Here is an interesting test based on the extreme brake failure of the Nismo 370's brakes at the 2009 Lightning Lap. My 2009 WRX also had significant brake failure, which also happened in their test. I did not crash, because I was driving the twisties here in NorCal at a slower speed... but my experience makes me not 100% agree on the original post in this thread...
Check out the article:
Anyhow, there is no doubt upgrading lines, fluid and pads will result in better braking performance and shorter stopping distances.