What are the differences between FADEC and EEC systems?
The EEC is the Engine Electronic Controller, the digital processing heart of the Full Authority Digital Electronic Controller. Kind of like the microprocessor in a digital computer. From The Jet Engine by Rolls Royce, 5th edition:

 

The EEC is dual redundant with all subs-systems such as sensors, cables etc duplicated, so that a single fail leaves the system fully operational. It is housed either in the airframe, or like in civil airliners on the engine, leaving it in need of protection of extreme circumstances:


Temperature - ice and tropical heat.
Electromagnetic radiation - lightning and airport radar
Engine vibration




The FADEC monitors inputs such as:


Shaft speeds
Engine temperatures
Oil pressures
Actuator positions
Power setting


and then sets fuel flow, variable stator vanes, and air bleed valves.