Well as a former Tennessean I felt compelled to answer. My brother went to Memphis and my bestfriend goes to UTK. Here is what I have heard..
UTK- Good school and solid education. Some people get bored because Knoxville is defn. a university town. It is a good size but mostly activities for 20-30 crowd is generated around the college. If you like outdoor activities it is a great place because the Smoky Mountains are very close. My friend likes it but says it is a little conservative for her taste but everyone is generally open and accepting of other people's views. UTK places well in the South,esp. obviously in TN, NC, and GA.
Memphis- Not ranked the highest but boasts the highest bar passage rate for the state even over Vandy. They focus on practical application not so much theory. My brother loved the clinics in particular the pro bono work he did but most of he loved Memphis. The music, rock and jazz, scene in Memphis is fantastic. The city is a very large and also has Rhodes College in addition to a couple of other smaller Christian colleges around it. Nighlife is great... Beale Street for the partiers. I had a friend that liked it because gambling was close. In terms of after school prospects, I am not really sure because my brother and my friend had really good contacts. My brother does corporate real estate law in Naples and Miami and makes tons of freaking money (me very jealous). And my friend who went there worked for some Congressmen before and they hooked him up with a good job in Nashville.
I hope this info helps a bit. Not much other than impressions...take it with a grain of salt.