I assume we are confining this to the BCS era. Since 1998:

Boise St. is 135-25 overall. 8-8 vs. ranked teams. 9-7 vs. teams that finished ranked. They have finished ranked 6 times. They have a 6-4 bowl record including 2 BCS wins.

TCU is 119-38 overall. 12-8 vs. ranked teams. 9-10 vs. teams that finished ranked. They have finished ranked 7 times. They have a 7-4 bowl record.

Utah is 110-43 overall. 11-8 vs. ranked teams. 6-12 vs. teams that finished ranked. They have finished ranked 4 times. They have a 8-0 bowl record.

BYU is 101-58 overall. 6-20 vs. ranked teams. 2-24 vs. teams that finished ranked. They have finished ranked 5 times. They have a 3-5 bowl record.

For my money TCU has been the best nonBCS program.