I see two people voted for the Nucks, who entered the NHL with the Sabres. I'm really interested in the reasoning behind selecting the Nucks over the Sabres? Even if you don't agree with the Sabres as the first choice, I think it's quite clear they've have a historical edge over the Nucks.
A successful franchise means a strong bottom line to me. The Canucks have only really been close to the cup once but have been sold out for years.
In the modern era (post-Bettman) definitely the Sharks. Have been contenders for the President's Trophy for many years now, some impressive winning streaks, strong 1st/2nd line, excellent rebuild, but have never made the Stanley Cup finals.
Including all eras pre-Bettman probably the Blues. Longest playoff streak in the league, made the Stanley Cup finals a few times and had a long history of success despite adversity in facing the quality of available players (expansion/early '70s), problems at the gate (late '70s/early '80s) and with personnel (mid-'90s with Keenan/Gretzky/Pronger etc.)
After those two and a fair ways down probably the Canucks, Sabres and maybe the Capitals. The pre-NHL Jets could've probably rivalled most NHL teams at the time (cept maybe Montreal or Boston) but after they got dismantled in the merger =\
Frankly, I voted for Vancouver without backchecking all the seasons and because they somehow came "closest" to winning the Stanley Cup in 1994. Rather than a solid reasoning, I will try to defend my vote from being an embarassment and point out that the Canucks had more Division titles than Buffalo and prepared their organisation for a quite successful period right now.
The numbers just don't add up. They both entered the NHL in 1970, so they are directly comparable, and the Sabres are clearly more successfull