The Thinline made in the '60s (specifically introduced in 1968) is equipped with the same pickups as a regular single-coil Telecaster, featuring a crisp and sharp sound. On the other hand, the '70s model (revised in 1972) is equipped with two Fender Wide Range Humbuckers.
As for the thickness of the sound, as you might imagine, it is overwhelmingly thicker, warmer, and more powerful than a regular single-coil. However, it is different from a Jazzmaster's single-coil (which is wide, bright, and has a jangly metallic attack), and compared to standard humbuckers like those on a Les Paul, it has better high-end clarity, featuring a sound where unique cut-through and semi-hollow resonance (an airy feel due to the semi-hollow construction) coexist.