It's the focus of this week's Hot Button, and Tim MacMahon goes toe-to-toe with ESPNBoston's Mike Reiss to debate the topic.
It's not an easy one. Each team won three Super Bowl championships during their decade of dominance.
MacMahon points out that at the height of their power, the Cowboys had a 49-15 record from 1992-1995. Meanwhile, on the other side, the Patriots were 48-16 from 2001-2004.
Reiss argues that the Patriots were more clutch, won with a young quarterback and did it with one head coach instead of two. But most of all, the Pats were able to maintain their excellence longer, while the Cowboys have all but fallen off the face of the playoff earth.