Let's take a look at some history. After all, that is what fans of both teams like to talk about.
Lou Holtz was the head coach of Notre Dame from 1986 to 1996. That's 11 seasons. Over that period, Notre Dame went 100-30-2. That's 9.1 wins a season.
Bo Schembechler (RIP) was the head coach of Michigan from 1969 to 1989. Over that period, Michigan went 194-48-5. That's 9.23 wins a season.
Now, let's look at what each program has done since their historic head coaches have retired.
Michigan w/o Bo: 8.9 wins per season over 19 seasons. Loads of NFL talent. Two Heisman Trophies. A large amount of NFL stars and/or starters. A National Championship in 1997. In 16 games against Notre Dame, they are 7-8-1.
Notre Dame with w/o Lou Holtzsch: 7 wins per season over 12 seasons. 0-7 in bowl games. In 10 games against Michigan, they are 5-5. No consistency in terms of staff or any sort of lineage between eras.
To put it simply, Michigan needs a Michigan Man. They need someone who understands Wolverine football like Jim Tressel understands Buckeye football. Someone like Brady Hoke would turn the Michigan program around. Notre Dame has no Notre Dame Man. The closest thing to a Notre Dame Man was Urban Meyer. He went to Gainesville, not South Bend.
As Michigan is more likely to find it's identity than Notre Dame, Michigan is in a better position.