They outshot opponents by an average of 11 per game during the regular season and 13 per game in the postseason. I don't think people quite appreciate or understand how ridiculous those numbers are. The phrase "puck possession" gained popularity because of those Detroit teams.
As with most great teams, it started with their best players. They had two 90+ pt, Selke finalist centers and a top 5 defenseman of all time. Babcock could control matchups. He could play Datsyuk/Zetterberg together against your top line if he had last change or he could put them on their own lines and not lose a minute of sleep. I'd argue that all three of them were Top 10 players league wide that year. That's a good starting point as to why Detroit was so good.
Then the depth was there. You had specialists: Draper was dominant in the dot, Holmstrom and Franzen were among the best net front guys. You had a mixture of skill and grit throughout the lineup. The postseason 4th line was a microcosm of that: Hudler-Helm-McCarty. Skill, speed, and toughness.
And it just all came together and worked. They completely bought into Babcock's system and rightfully so. That was Detroit's 4th Cup team of that whole era, but none of them were quite like that 08 group. We keep saying machine like, but that's really the only way to describe it.
And yes, Anaheim was a great foe during those few years.