Hello, 

Electrical and Electronics Engineering branch deals with Electrical technology and machines, circuit analysis, electronics, electromagnetism, electrical engineering materials, instrumentation, control systems, power engineering and transmission and distribution.One has to study electrical engineering as well as electronics. 

ECE branch mainly deals with analog transmission, basic electronics, solid state devices, microprocessors, digital and analog communication, analog integrated circuits, satellite communication, microwave engineering, antennae and wave progression. It also deals with the manufacturing of electronic devices, circuits, and communications equipment.

EEE: Electrical graduates are employed in Electricity Boards/Utility companies responsible for installation, maintenance, operation of power handling equipment and systems. Industries manufacturing large electrical machines and equipment employ engineers in design, production and testing.  

ECE: In ECE, the scope to land into government jobs is great. An electronics engineer can find a job in Central Government, State Governments and their sponsored corporations, private industries dealing in manufacture, sales and services of electronics consumer goods and appliances. Additionally, electronics engineers are also absorbed into the broadcast industry, research establishments, and defence.

Electronics and Commination Engineer gets recruited in PSUs such as BEL, DRMC.MNCs such as Siemens, Texas instruments, Intel, NVidia, Philips Electronics, Motorola, Samsung and Flextronics.DRDO, ISRO and IT companies like Infosys, TCS, Wipro, Accenture, HCL Technologies and Tech Mahindra, EXL.

Electrical and Electronics Engineer gets recruited in PSUs such as BHEL, NTPC, DMRC, NHPC, Power Grid. State electricity boards like APTRANSCO, APGENCO. Private companies such as Crompton greaves, Siemens, Hitachi, Jindal steel and power, reliance, I&T, TATA and Samsung engineering.

I've done a bit of differentiation between the two branch, in terms of what's it's all about and job prospects, the question of better rests with you, since job prospects of a field go hand in hand with the interest of a candidate as well, in the particular branch. 

Hope, this helps. 

Thank you!