I have some data on this, regarding playoff performance.
QB vs average defensive performance (defensive home/away split stats or combined if neutral):
1966-1993 have to manually calculate
1994 Green Bay D passer rating playing at opponent: 73.8
Aikman passer rating: 121.1, above (1-0)
1994 San Fransisco D passer rating playing at home: 67.8
Aikman passer rating: 68.1, above (2-0)
1995 Philadelphia D passer rating playing at opponent: 62.4
Aikman passer rating: 101.6, above (3-0)
1995 Green Bay D passer rating playing at opponent: 93.2
Aikman passer rating: 107.5, above (4-0)
1995 Pittsburgh D passer rating playing anywhere: 75.5
Aikman passer rating: 108.8, above (5-0)
1996 Minnesota D passer rating playing at opponent: 83.8
Aikman passer rating: 67.9, below (5-1)
1996 Carolina D passer rating playing at home: 53.6
Aikman passer rating: 37.4, below (5-2)
1998 Arizona D passer rating playing at opponent: 89.9
Aikman passer rating: 37, below (5-3)
1999 Minnesota D passer rating playing at home: 77.3
Aikman passer rating: 70.7, below (5-4)
2003 Carolina D passer rating playing at opponent: 78.6
Carter passer rating: 56.9, below (0-1)
2006 Seattle D passer rating playing at home: 75
Romo passer rating: 89.6, above (1-0)
2007 New York D passer rating playing at opponent: 74.9
Romo rating: 64.7, below (1-1)
2009 Philadelphia D passer rating playing at opponent: 77.8
Romo rating: 104.9, above (2-1)
2009 Minnesota D passer rating playing at home: 84.2
Romo rating: 66.1, below (2-2)
2014 Detroit D passer rating playing at opponent: 85.6
Romo rating: 114.0, above (3-2)
2014 Green Bay D passer rating playing at home: 76.7
Romo rating: 143.6, above (4-2)
2016 Green Bay D passer rating playing at opponent: 107.4
Prescott rating: 103.2, below (0-1)
2018 Seattle D passer rating playing at opponent: 95
Prescott rating: 83.6, below (0-2)
2018 LA D passer rating playing at home: 100.3
Prescott rating: 99.2, below (0-3)
Beuerlein, White, Staubach, etc. no info yet.
Aikman was 5-4 (incomplete) above average passer rating in playoffs.
Carter was 0-1 above average in playoffs.
Romo was 4-2 above average in playoffs.
Prescott is currently 0-3 above average in playoffs.