Which branch at IIEST Shibpur has the biggest package?

You will definitely be able to fetch a really good package by pursuing one of the many streams and courses offered at IIEST Shibpur. 

• If you are from the CS/IT branch, you can even bag an average salary package of around INR 10 LPA at Microsoft. 
• If you are looking mainly for the big package companies, you will have to go for the off-campus placement drive where companies like Google, Amazon, Flipkart, TI, and Directi usually visit. In the final year, you might see them in the campus placement as well.
• You can fetch CS jobs with good knowledge in Algorithms, programming, Systems Design. But keep in mind that different job profiles will need different skill sets.
• There are multiple options for big names for Mechanical students as well. Options like Tata Steel, Tata Metaliks are providing good packages for people from MET, EE, and Mechanical departments.
• Other options include Siemens, GE, or PGCIL for Electrical Engineering students where you can expect a package starting at INR 8 LPA.

Generally, the starting salary package of a Mechanical/EE/Civil/Met is lower than that of CS/IT graduates. Once you enter the industry, your pay will depend on the quality of work you deliver.

So, you should get into the branch of your interest and develop yourself in that field. The results will definitely be fruitful.