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Dear Sai,
I can totally understand your dilemma in this case as I have been through the same.
Now, you need understand that there are two important things to consider while seeking admission.
(i) A branch of your choice but from a not so good institute = Not much value.
(ii) A not so demanding engineering branch from a good institute= Not much value either.
In your case, both, the engineering branch and both the institutes are good and thus it will be difficult to tell which will be better. However, below are some key points
Regarding Branch:
Mechanical
Mechanical engineering has a lot of scope in India and abroad. Some of the areas where these people can utilize their capabilities include the following.
Automobile industry
Aerospace industry
Steel plants
Power generation industries
Communication sector
Railway departments
etc.
Some of the government departments where they can apply are:
ONGC
VSSC
ISRO
IOC
DRDO
SAIL
NTPC
etc.
Computer Science Engineering
Computer Science Engineering is a division of engineering which involves the principles and techniques of both computer science and electronics engineering. It includes testing and designing of computer components.
Some of its specialized fields are: -
Networking
Game Systems
Customer service
Database systems
Embedded systems
Operating systems
Computer Validation
Software engineering etc.
Scope:
The rapid growth of information technology has made computer industry, one of the fastest growing segments. Because of it, there is a huge demand for computer engineering professionals for the development of faster hardware components, new communication systems and software. Computer Engineers with a high percentage of mark and good communication skills can be simply employed in top companies. Software and IT companies are the major employers of these graduates. Some of the top companies such as Microsoft, Google, HCL, Infosys, Wipro, TCS and Mahindra offer a very high salary package.
For details regarding institutes, refer to my below comments.

Dear Nithin,
In order to pursue a career as an Environmental engineer or Energy Optimization Engineer or an Energy Analyst, you can pursue a Bachelors in the following branch:
Civil Engineering
Agricultural Engineering
Chemical Engineering
Mechanical Engineering
Environmental Engineering
Petroleum Engineering
Petroleum Technology
Petrochemicals Engineering
Petroleum Refining & Petrochemicals Engineering
After completing your engineering, you can find jobs in public sector departments such as Forest department, urban development, Industries, water resources and agriculture. Distilleries, fertilizers plants, water treatment industries, refineries, textile mills, mines and food processing industries are other private sector areas that use the service of an Environmental Engineer. Also some international firms working for environment related projects render their service. One can also work as a journalist after completing this course. After completing this course, the graduate can get good jobs in both central and state population control boards.
Many public sector departments also recruit Environmental Engineers. Some such departments hiring an Environmental Engineer are listed below.
Forest department
Urban development
Industries
Water resources
Agriculture
Population control board
Those working with public sector are rewarded with good salaries and benefits.
Hope this helps.
Thanks
All The Best.