What part of Kentucky? You say an hour shy of Lexington? Are you in Morehead or around there?
I am from Louisville and just graduated from UK in Lexington. Here is how Verizon tends to roll in Kentucky: In areas Verizon serves, they are far better than AT&T. AT&T is a colossal trainwreck in Louisville and Lexington. Verizon is hands-down the better choice in Kentucky if you are in their native network (not Appalachian or Bluegrass, although Bluegrass is very good). If you were in an Appalachian territory and AT&T had 3G there, I would go that route, but since you are in native Verizon area, I can confidently say they will serve you better.
I pull LTE speeds of 60+mbps in Louisvlle on LTE, and 2.5+ on 3G on Verizon. Ditto for Lexington, and the 3G speeds are stellar along 64 as well. All of 64 between Lexington and Louisville is LTE, and I also know Ashland now has live LTE service. It is only a matter of time until they come through to light up your area as well. Verizon is very aggressive in Kentucky it seems.
If there is one thing I can almost guarantee, it is this: if you have Verizon bars in your house, your service will be faster than EDGE on AT&T. Moreover, all areas that currently have Verizon 3G (including your stomping grounds) will be LTE by 1 year from today, so I recommend you go with the new Verizon GS3 or any other VZW LTE phone.
For everyone above complaining about CDMA networks: why? How hard is it to hop online and change out an ESN? Harder than swapping SIMs, ok, but not difficult at all. Regardless, if you purchase an LTE phone from Verizon, you get the same SIM-swapping benefits.
Like Fraydog said, it sounds like Verizon is relatively un-congested there since you cannot find one person there with a VZW smartphone. That's probably a good thing- more bandwidth for you. If I could get out that way, I would stop by and run some tests for ya, but I got a whole weeks worth of work here in Louisville, so I can't.
Just know this: assuming you have Verizon 3G in your house:
-it will be faster than AT&T EDGE
-it will be more reliable than AT&T EDGE (voice and data)
-it will be 4GLTE by this time next year
Go to your closest VZW store and sign up, you have 14 days to see if the phone works in and around your area. If it does not meet your satisfaction, return it.
I feel confident VZW is the best choice for you going off how stellar they are in the rest of Kentucky. It is a shame AT&T has neglected our state (in regards to the lack of HSPA+ rollout and quality of the network in places they do have HSPA+ (Louisville especially)). With no help coming to your area soon from AT&T, I say give Big Red a shot- you'll most definitely be glad you did!
EDIT: one more thing. Even if Verizon's 3G ain't all that great at your place, 4GLTE will probably help with that, because even at one bar, the speeds can reach 5-6mbps, far more than you need to do most things. However, there is a very good chance Verizon will be better at your house today, and only get better next June with LTE.