Writing for North Carolina’s official athletics site, Adam Lucas calls the Kentucky-UNC rivalry the best interconference rivalry in all of college basketball.
An excerpt:
“Thanks to a variety of factors, the Tar Heels and Wildcats have the best inter-conference rivalry in college basketball. They’ve experienced similar levels of success, but the meetings have been infrequent enough to retain a sense of importance. Fans of both programs would probably tell you that other than the prolific winning, the two competitors are very different. Kentucky thrives as the lead dog in a hoops-mad state, while Carolina shares Tobacco Road with three other rivals. The Wildcats have had a succession of coaches since Adolph Rupp, while Carolina’s portion of the rivalry is built largely around Dean Smith.”
While this rivialary is a very good one, I think if you re-worded the question to: Who would UK rather lose to, North Carolina or Louisville, the fan base would overwhelming vote North Carolina. The fan base dislikes UNC but they hate Louisville, this, without a doubt, would make the UK-UL game, the best “inter-conference” rivalry in college hoops.