I'm not capping it, this discussion is fine, in the sense that there is reasonably respectful debate back and forth.
I have my own thoughts as far as metrics go on this:
Kenpom "A" games record: Carmody 23-132, 14.8%; Collins 37-127, 22.6%
Kenpom "B" games record: Carmody 35-42, 45.5%; Collins 38-44, 46.3%
Kenpom rest of games record: Carmody 134-36, 78.8%; Collins 118-17, 87.4%
Conference/BTT games record: Carmody 75-163, 31.5%; Collins 91-152, 37.4%
NCAA Tourney record: Carmody 0-0, N/A; Collins 3-3, 50.0%
Top-half conference finishes: Carmody 1; Collins 3
Top-50 offenses: Carmody 4; Collins 1
Top-50 defenses: Carmody 1; Collins 6
1st-team all B1G players: Carmody 2 (Jitim Young, John Shurna); Collins 1 (Boo Buie)
In my opinion, you cannot separate recruiting from coaching. If you are a good coach, you need to be able to both recruit players that can play in your system and also coach them up to win games.
Carmody had an offensive system that allowed his less-talented players to maximize their potential, but their peak was the NIT due to an inability to coach up defense and a lackadaisical approach to recruiting. He was never able to get more than one headline player in a class, and therefore never had the depth required to truly contend in the conference. At other schools, he likely would've been fired following the 8-22 record in his 8th season, but he got a second chance that lead to 4 NITs in a row.
Collins has a defensive system that has allowed his less-talented players to maximize their potential, and 3 times he has done what no other Northwestern coach had ever done. Collins had recruiting misses after his first class that nearly threatened to cut his time short at NU, but a second chance led to back-to-back Tourney bids and has set things up for the future.
I can't see any way in which Collins is not a better coach than Carmody or that he is not the greatest coach in Northwestern history based on what he has accomplished.