Electrical and Electronics Engineering

There are good branches and offers a lot of opportunities after completing your graduation. There are different perspectives in which you can compare two different departments, which obviously excludes what they deal with, because that cannot be compared.
Mechanical engineering:
Mechanical Engineering graduates can work in the automotive, aerospace, chemical, computer, communication, paper, power generation and almost all manufacturing industries. Mechanical engineers also work in maintenance and service profiles in all industries. Also they can choose teaching profession in universities and colleges. Mechanical Engineering have job opportunity in private sector and public sector (CSE branch doesn't give much options in public sector)
Top recruiters for mechanical engineer:
BHEL, BPCL, DRDO, Indian Oil, GAIL, NTPC, Ashok Leyland, Hona, Mahindra & Mahindra, Maruti Suzuki, Tata Motors, Infosys, L&T, DMRC etc. Below are job profiles in ME:
Design Engineer
Machine component designer
Technical Officer
Product Manager
Purchasing Officer
Sales and Maintenance Engineer
Computer science engineering:
Software engineers have been recruited by the IT majors like Tata Consultancy Services (TCS), Infosys, Wipro, HCL, Cognizant, Accenture etc. They were even recruited in the famous Silicon Valley in USA by top companies like Yahoo!, Adobe, Apple Inc, Google, Intel, etc. CSE branch doesn't have many options in public sector. Below are job profiles in CSE:
Computer Programmer
Systems Analyst
Software Developer
Hardware Engineer
Consultant
System Engineer
System Designer
Networking Engineer
Database Administrator
Web Developer
E-commerce Specialist
Programmer
In India, the job prospect of a CS graduate is more, compared to ME, owing to the presence of a large number of IT companies and their demand for man source. So even if you don't make it to a tier-1 college, you will land a decent job, most preferably in an IT major/MNC. Though the salaries will differ a lot from that of tier-1 colleges. On the other hand, there are not a lot of core companies (for ME). So, even if you are not in a tier-1 college it won't matter. You have to be exceptionally good in your curriculum, score high and develop deep understanding of the subject as most of the top core companies recruit through GATE.

Shah don't go with which stream is better. Go with what you want do after studying B.Tech. You may take following considerations. If you like computer, want to build crazy application or something related to software go with Computer Science engineering. If you like playing with machines/motors or electricity go ahead with Mechanical engineering. Or Electrical engineering. If you are India, after studying Electronics and communication engineering most of the students gets job/work in IT companies. Only few percent gets chance in electronics companies. So I would suggest, better to study Computer Science engineering. If you want to sail through vast sea go with Marine engineering. If you have not decided what you want to do after B.Tech, sit for one or two days and decided what you want to do. If still confused, select any of the engineering mentioned in point # 1, 2 and 3 (Computer Science, Electrical, Mechanical, or Electronics). Best of luck.