Perhaps my judgment on this has been recently skewed because I spent a lot of time around A&M fans in Omaha, but I think it is quite possible that the emotion around the Texas/Texas A&M rivalry exceeds that of the Iron Bowl and is the most heated rivalry in the country. The reason I say "emotion" instead of hate/dislike is because that rivalry isn't simply about dislike.
Texas fans look at A&M as an object of disgust, like gum on the bottom of their shoe. A&M fans look at Texas with a truly bizarre, clinically-diagnosable range of emotions. Hate, envy, jealousy, contempt, and paranoia. I've never seen anything like it in any other rivalry. Two-thirds of A&M's fight song is taking shots at Texas and not even about their own school. To say that they have a hang-up with Texas doesn't even begin to describe it. We ran into probably 10 different groups of A&M fans over 3 days and within 90 seconds of each interaction, they brought up Texas on their own to slam them in some way. It was funny the first couple of times, but as every single one of them kept doing it I was like "Guys, they aren't even here." lol