Vaughn is right,except that with the 4l80E you will need a computer. The computer controls shifting through solenoids instead of mechanical valves as in the TH350/400 and 700R4.
The 700R4 uses the computer to control the Torque convertor lockup, but you can buy an aftermarket kit to by pass that function. The 4l80E was designed to work with a computer.
Be sure you get a later model 700R4 if you go that route. The early ones (86-88) were known as the Turbohandgrenade for a reason