Electronics and Communication Engineering

ECE is about electronics and how the different electrical components (Microprocessor, RAM etc.). Communicate with each other. It has more Physics in it. There is a little programming involved but not much. CSE deals with telling these components what to do and when to do it; by programming them. It has a lot of logic involved and Maths too. Eg: In designing a tablet/phone, all the hardware work is done by the ECE people and all the software stuff (making the different components like RAM, processor talk to each other, and the Operating system) is done by the CSE people. Both are inter-dependent. Placement wise, ECE is a little better than CSE as it has more offers in the public sector (government jobs). Also ECE is considered to be somewhat of a evergreen branch. If you do specialisation (eg M.Tech in VLSI design) after doing B.Tech in ECE, there is a great demand in the market for such people. ECE person can also get a job in IT; but this is not the same level as a job a CSE engineer can get. Eg: Intel, AMD, BHEL (and many other government companies)
CSE also has very good placements and the avg salary is higher than ECE. But it is not an evergreen branch. Eg: Google, Microsoft, Infosys, etc. People say that ECE is more difficult than CSE. But I don't really believe that; it all comes down to your passion. If you love CSE, you will find ECE hard and vice-versa. In the end, I would say it all comes down to interest. Yes I agree ECE has an edge over CSE when it comes to placements. But if you excel in CSE and have true passion for it, you will probably do better than most ECE people also. It is on your interest what you want to go for.