700R4 is the same thing as a 4L60E, they just use a new name, plus it is electronically controlled (the meaning of the E in the name). 4L80E is the TH400 with an overdrive gear on it. You can think of the 700R4 (or 4L60E) as a TH350 with an overdrive gear. It's an oversimplification, but it makes it a lot easier to understand for most people.
Use the 700R4 for most applications. IF you REALLY do a lot of towing or have a heavy vehicle use the 4L80E.