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The Dolphins were a lot more well-rounded team. They had both the #1 offense and #1 defense. On defense, they were equally dominant against the run and pass. Their rushing offense was one of the most dominant of all time ranking 4th in yards since 1940. They had two 1000 yards rushers in a 14 game season. You might think they weren't great at passing but Morrall's QB rating (91.0) was 137% of the league average which is nearly the same as Brady's at 141%. Incidentally, Morrall's 91 rating that season is higher than Brady's career playoff rating of 89.8. Think about all the advantages modern players have and let that sink in for awhile.
The Patriots had a good passing attack but were pretty average at running the ball. They also were pretty average at stopping the run ranking 10th and allowing 4.4 yards per carry.
Strength of schedule doesn't mean that much especially when you're talking about undefeated teams. They have no say in who they play. Regardless, it wasn't like the Patriots were playing an especially difficult schedule. Pro Football reference's system has their schedule at .4 which is about average.