From 2010-11 to 2018-19:
Most Regular Season Point Totals:
1. Pittsburg - 908
2. Washington - 894
3. Boston - 887
4. St. Louis - 875
5. Tampa* - 868
(Anaheim Ducks next with 859)
Most Regular Season Wins:
1. Pittsburg - 419
2. Washington - 408
3. Boston - 403
4. St. Louis - 403
5. Tampa* - 402
(San Jose Sharks next with 390)
Most Postseason Wins:
1. Boston - 62
2. Pittsburg - 59
3. Washington - 53
4. San Jose* - 52
5. Chicago - 51
(New York Rangers next with 47)
Stanley Cups:
Chicago - 2 (3 if you count 09-10 season), Pittsburg - 2, Los Angeles - 2, Boston - 1, Washington - 1, St. Louis - 1
I'd rank them:
1. Pittsburg (2 cups, dominant in post and regular season throughout the decade)
2. Chicago (2-3 cups, dominant in regular and post season for the first 2/3 of the decade)
3. Los Angeles (2 cups, dominant postseason team for the first half of the decade)
4. Boston (1 cup, dominant in regular and post season throughout the decade, multiple cup appearences)
5. Washington (1 cup, dominant in post and regular season throughout the decade)
6. St. Louis (1 cup, dominant regular season team throughout the decade)
And then: (7. San Jose), (8. Tampa), (9. New York) (10. Nashville)
Based on a combination of regular and post season success throughout the decade