Weiss is in his third year I believe and last year ND went to the Fiesta Bowl. I don't think Willingham went to a bowl, again I could be wrong.
I just looked at their records. If my numbers are correct, it looks like this:
02: 10-3 - Willingham (lost bowl game)
03: 5-7 - Willingham
04: 6-6 - Weiss (lost bowl game)
05: 10-2 - Weiss ( lost bowl game)
So, Willingham went 15-10, lost a bowl game, and was fired. Weiss went 16-8, lost two bowl games, and was rewarded with a contract extension.