During the years that I lived in Georgia, I would joke that it seemed like there was an ongoing conspiracy to convince me that Chattanooga was cool. People in Atlanta don't shut up about Chattanooga; they're always telling you that it's cool and affordable and close to great hiking. Traffic in Chattanooga is bad and I don't think it's nearly as cool as people want to believe it is (just from a sociological perspective, actually cool places don't tend to vote Republican), but it is a nice town and I've enjoyed the time I've spent there. When I would take road trips north, I would often stop in Chattanooga for breakfast on the way up or for dinner on the way back home. One regret I have is that I never made it out to Cloudland Canyon, which is in the vicinity.
By contrast, I've only so much as been through Knoxville once, and that was on a long-distance bus five years ago. At the time it struck me as the ugliest city I had ever seen, although I'd be willing to revisit that characterization. A friend of mine was a high school teacher in Knoxville for a few years and she liked it a lot, but on the whole I haven't heard people talk about Knoxville in anything like the tone they use when they talk about Chattanooga. I also don't really care for their shade of orange.
I'm willing to acknowledge that I don't know Knoxville well and set that equal, but even still, Chattanooga has the great municipal wi-fi. I don't know if that's something people elsewhere know about, but in Atlanta the wi-fi in Chattanooga is a constant subject of discussion. Probably more importantly, it's a lot closer to the big city. I'd take Chattanooga.
Chattanooga does have some nice places to visit (it's only about an hour and a half drive for me). I've always liked the aquarium there more than the one in Atlanta.