I was speaking about BWH vs. Stanford match (not Duke), but decided to PM. To be comprehensive and hopefully helpful, here is the summarized match list from this past year for competitive specialties (just because I'm too lazy to summarize all specialties) at each program. Interpret as you will.
Duke
Cardiology - Duke (5), UTSW (1), Iowa (1), Cleveland (2), UAB (1), UNC (1), NYU (1), Michigan (1), Vermont (1), BI (1), Mt Sinai (1), Wash U (1)
Oncology - MD ANderson (1), Duke (1), MSK (1), Oncology (1)
GI - Ohio State (1), Duke (3)
Pulm/Crit Care - Emory (1), Duke (3), NYU (1)
Brigham and Women's Hospital
Cardiology - BWH(3), MGH (1) Duke (1), Stanford (1), Cleveland Clinic (1), Columbia (1), Penn (1), NW (1)
Oncology - DFCI (6), MD Anderson (1), MSK (1), Stanford (1), Penn (1), UCSF (1), Yale (1)
GI - BWH(2), Michigan (1)
Pulmonary - Penn(1), UCSF (1), BWH (2)
Stanford
Cardiology - Stanford (4), UC Irvine (1), NW (1), Cleveland (1)
Oncology - Stanford (5), UCLA (1)
GI - Stanford (2), UCLA (1), UCSF (1), UWash (1)
Pulmonary - UWash (1)