Interesting tidbit. Here are the scores of the Pats' 7 Super Bowls in the TB/BB era.
W, 20-17
W, 32-29
W, 24-21
L, 14-17
L, 17-21
W, 28-24
W, 34-28
So in order, their points allowed in these 7 SBs, from most to least, and the result:
29 (vs Car) - win
28 (vs Atl) - win
24 (vs Sea) - win
21 (vs Phi) - win
21 (vs NYG) - loss
17 (vs NYG) - loss
17 (vs StL) - win
So in the three games where they gave up the least number of points, they won two of them. In the three games where they gave up the most points, they won all three.
So....defense wins championships? Well, kinda sorta. In the Atlanta and Seattle wins, clearly the defense came up HUGE in the second half, despite allowing higher numbers of points, and of course 7 of Atlanta's points came on a pick-six.
On the flip side, here are their points scored, and the result:
34 (vs Atl) - win
32 (vs Car) - win
28 (vs Sea) - win
24 (vs Phi) - win
20 (vs StL) - win
17 (vs NYG) - loss
14 (vs NYG) - loss
So in that view, their offense seems to hold the key. When they score points, they win. When they don't, they lose.
EDIT: Their points scored in their last two Super Bowl title runs:
2014
35 (vs Bal)
45 (vs Ind)
28 (vs Sea)
AVG: 36.0
2016
34 (vs Hou)
36 (vs Pit)
34 (vs Atl)
AVG: 34.7