Having lived in both cities, I can tell you that as a climber, Chattanooga is a much, much better city than Knoxville. Twall, Suck Creek,and Sunset Park, all fantastic trad destintations (Suck Creek even has multipitch)within 20 minutes of downtown, There's Leda,with good sport and trad, about 20 minutes away; LRC with world class bouldering 5 minutes from Leda; and Fosters 45 minutes away with great sport climbing. North Carolina trad isn't further than 3.5 to 4 hours.
Knoxville on the other hand has the Obed about an hour and 20 minutes away, Big South Fork 2.5 hours out, Devil's Racetrack (not really worth the drive) 45 minutes away, but the closest climbing, Cherrokee bluffs, 5 minutes from downtown, is now closed. Knoxville is also no where near 2 or 3 hours from the Red or the New.
All in all, within a 30 minute drive from the downtowns of each city, Chattanooga has 500-1000 routes, Knoxville has about 25.
As far as the cities and schools themselves go, Chattanooga is a much more enjoyable city, with a better downtown area and less of an obnoxious party scene. There is a larger outdoor scene and the art scene isn't bad either. The food in Chattanooga is more local than Knoxville. Chattanooga is also 2 hours from Knoxville, Atlanta, Nashville, and Birmingham if you're concerned about the music.
Knoxville has better suburbs and a larger party scene if you're into that, and a larger music scene. There might be a larger job market in Knoxville for teachers. The food scene in Knoxville sucks. All chain restaurants, not many local gigs.
UTC is a very good school, but academically, Knoxville is better.
So, if I were you, I would choose Chattanooga. I did. I don't regret it at all.