Great question. This answer has changed a lot over the years. I will give you a complete breakdown.
I first became aware of Kansas State football as a thing in 1992. I went to games for years before that, but the stadium was mostly empty and for running around and pushing matchbox cars down the stairs and messing around with rabid Willie. I went through year by year and looked at the schedule and spent 5-30 seconds putting myself back in that year. Some patterns emerged:
Universal Rules:
It hurts much more when you lose at home.
It definitely hurts much more to get dominated physically, I never got mad at Texas Tech because of this I would just LOL/check out.
Baylor is the exception because of 1) what the did to us in '12 2) stupid Phil Bennett and his agro/cheap shot/hold/PI every play D
All things considered, it would be significantly more demoralizing to lose 42-0 to OU with Perine running for 250 than to lose 70-21 to Baylor with a bunch of TOs and quick strike TD bombs.
Other observations:
Until we beat Nebraska, that was the biggest game by far every year. Only when we fell back down did Nebraska re-emerge as the most hated team I wanted to beat/humiliate/root against in every other game.
Oklahoma basically took Nebraska's spot, but Colorado kind of took our spot and so Colorado really replaced Nebraska as the rival as we didn't play Oklahoma every year and we descended in to the depths of the Big XII North.
Only when we were elite in 2000 and 2003 did Oklahoma surpass Colorado, in 02 we didn't play them and in '03 it is only because of the Big XII title game that we were even able to sabotage them.
The mid-late aughts were dominated by losing to KU under Mark Mangino which was very unpleasant.
Nebraska leaving the Big XII and Bo Pelini (and our impotence against that disgusting combination) brought them back up to most hated
Oklahoma and Baylor are now the most hated with Baylor being the most likely continuing leader as Bob Stoops has mostly turned in to a parody of himself and we have beaten them enough to make it ok.
THE LIST
1992-1997 Nebraska was the most hated team
1998 Texas A&M
1999 Nebraska
2000 Oklahoma
2001 Colorado
2002 Colorado
2003 Oklahoma
2004 Colorado
2005 KU
2006 KU
2007 KU
2008 KU
2009 Nebraska
2010 Nebraska
2011 Oklahoma
2012 Baylor
2013 Oklahoma
2014 Baylor
2015 Baylor