Assuming the OP meant the Dead Puck Era (1995-2004), I'd have to go with the Wings, though AINEC in favor of either team is a wrong answer. And though the Wings having a 3-2 cup edge helps, it's not the end all be because I rank the Avs above the Devils during this era, despite them also having a 3-2 cup advantage.
When comparing other categories for this era, the Wings mostly come out on top of the Avs. Here's how Detroit, Colorado and Dallas compare from 1995-2004 in categories besides cups:
#1 seed in the Western Conference:
1. Detroit: 4 (95, 96, 02, 04)
2. Dallas: 3 (98, 99, 03)
3. Colorado: 2 (97, 01)
The other winner was St. Louis in 2000 (President's trophy as well)
President's trophies:
1. Detroit: 4 (95, 96, 02, 04)
2. Colorado: 2 (97, 01) and Dallas: 2 (98 and 99)
Conference final appearances:
1. Colorado: 6 (96, 97, 99, 00, 01, 02)
2. Detroit: 5 (95, 96, 97, 98, 02)
3. Dallas: 3 (98, 99, 00)
Conference champions:
1. Detroit: 4 (95, 97, 98, 02)
2. Colorado: 2 (96 and 01) and Dallas 2 (99 and 00)
Playoff series against each other:
Colorado vs Detroit: 3-2 Avs
Colorado vs Dallas: 2-1 Stars
Dallas vs Detroit: 1-0 Wings
As we can see, the Wings come out on top in most categories, in addition to cups.
As I said before though, I do rank the Avs ahead of the Devils during this era. The Devils playoff performances from 1996-99 (one playoff series win) drop them below the Avs in my book, in spite of them having one more cup. Plus the West was much tougher than the east. The Devils were the only big 4 team in that era in the East. The Avs lost 4 times in the WCF, twice apiece to Detroit and Dallas, which IMO costed them at least 3 cups. They'd be favorites over the 97 Flyers and heavy favorites over the 99 Sabres and 02 Hurricanes, while the 2000 Devils would've been a tossup like their finals the next season.
All in all, here's how I rank the big 4:
1. Detroit
2. Colorado
3. New Jersey
4. Dallas
And while I've seen many what if scenarios here, mainly revolving around one or more of the WCF game 7's the Avs lost, I think the game that would've impacted the rankings the most was game 7 of the 2001 SCF. If the Devils win it, they would've undisputedly been the best of this era, not only having the most cups but also beating all of the other 3 in the finals. Meanwhile, the Avs might be below the Stars in this scenario. Each would've had a single cup, but perhaps the Stars winning both of the WCF they played against each other would've given them the edge in this case.
Of course there was the trade that sent Kozlov and a 1st round pick to Buffalo for Hasek. But either way, let's remember one thing, if a team "bought" the Cup, good for them. It isn't as if the Rangers didn't try over this entire era. My Leafs tried. Detroit was just a place that players knew wanted to win. It will surprise some people looking back, but that 2002 team had trouble in practically every series they were in. 1st round they are down 2-0 to Vancouver and if Lidstrom's center ice shot doesn't go in during Game 3 who knows what happens. They controlled St. Louis rather easily but were down 3-2 against Colorado. Then in the final, despite it being a 5 game series it was more like the 1993 Cup final in the way that the earlier games were far from a done deal. Detroit loses Game 1, then won Game 2 but didn't break the tie until 5 minutes left in the game, then scored with a minute left in Game 3 to tie it and needed triple overtime to win while Carolina had a glorious opportunity with a power play in the second overtime. After Game 3 it was a done deal I think, but those first three games were closer than some might remember. They put more of a scare into Detroit than you would have thought.
I agree that the notion of the 2002 Wings being a bought team is overblown. It's not like most of them were in their prime, which would've been financially impossible to have them all on the same team, even for a big spending team like Detroit in the pre salary cap days. Big Phil is right about them facing struggles in every series outside of the St. Louis one, and there were people who questioned whether a team as old as them could survive the grind required to win a cup.