I didn't do any exhaustive research so there are likely plenty of lesser names missed, but here's a comparison of goalie acquisitions as GM by Nonis and Burke, followed by some brief analysis...
Hartford - Sean Burke (trade) (very good)
Vancouver - Keven Weekes (trade) (terrible)
Vancouver - Dan Cloutier (trade) (bad)
Vancouver - Alex Auld (trade) (bad)
Anaheim - Jonas Hiller (undrafted free agent) (very good)
Toronto - Martin Gerber (waivers) (terrible)
Toronto - JS Giguere (trade) (mediocre)
Toronto - Jonas Gustavsson (undrafted free agent) (terrible)
Toronto - Ben Scrivens (undrafted free agent) (to be determined)
Roberto Luongo (trade) (elite)
Cory Schneider (1st round draft pick) (potentially elite)
Basically, Burke made only one good trade, his first one, way back in 1992, an era when elite goaltending was not really as essential and goal scoring was the name of the game. In Vancouver he made trade after trade for terrible goaltenders. That didn't work. In Anaheim, he was lucky in that he already had a stud goalie in Giggy to start and never had to seek a no. 1 goalie. With no pressure, and already have Bryzgalov as a backup, he acquired Jonas Hiller for no cost as an unsigned and untested European free agent and was very fortunate to see that signing turn into gold. Unfortunately this experience would spoil him for Toronto---the lessons he learned from this is that signing undrafted goalies is the way to go and you'll sure to strike gold if you keep at it. And he also had this propensity to bring back players he liked (I call it Brad May syndrome) regardless of their current capabilities---and so Giguere was the stop plug for a few seasons.
Meanwhile, Nonis seems to know goalies. Or, has luck and small sample size. Anyway the whole point is that if Dave Nonis says you should trade away all your best players to Vancouver for Roberto Luongo, he's probably right and you should DEFINITELY do that. The end.