I wasn't cognizant during the Burns Leafs but Quinn's Leafs were highly entertaining. Great cast of players and characters. Quinn himself of course was a character, skilled players in Sundin, Kaberle, Mogilny, McCabe, warriors like Tucker, Roberts, Domi, and in net Cujo and Belfour with their unique mask designs. And that's just the core guys, from 98-99 to 03-04 there were a ton of interesting players that made this team a joy to cheer for. "Stumpy" Thomas, Berezin, Yushkevich, Markov, Green, Corson, Belak, the list goes on.
I've seen footage of the Burns era Leafs, specifically th3 '93 run, and that era will always be the one that got us as close as we've been to Stanley Cup glory and resurrected this franchise after the nightmare that was Ballard. But Quinn's teams being successful for longer I think gives him the edge.