Fender Tele's with a humbucker in the neck position can be one of the most versital guitars going. I have a fat tele also, plus I have modified several teles for that sound.
Scotty Anderson plays an old Tele like that with Special pickups by Jim Rolfes, I think his name is.
That guitar can sound like a jazz box, a screaming tele or anything in between, and of course Scotty's right hand technique has a lot to do with it.
For some sound samples click here.
http://home.cinci.rr.com/jpeel/soundbites.html