Colleges in Howrah

You can choose MME.
I don't know much about the IIEST Shibpur College and I couldn't evoked about this institutions too
But I can give some suggestions as an alumni of metallurgical engineering from VNIT, Nagpur don't prefer MME instead opt for any circuit stream in the other college as per your preferences.Why I'm suggesting you is that there are no placements for metallurgist students since batch of 2013 to 2014 onwards there is no decent placement and everyone take the admission merely wanted to land with decent package after their graduation and no one rely wanted to learn the engineering subjects such a huge investigated of four years life and except some topper dudes 510% out of 100% of total strength of the distinct branches .
Basically MME comes under manufacturing sector like making gears and launching new machines for implementing the new innovative ideas to develop new technologies with help of producing quality and flawless output and making every customers compensations etc and its giving sounds good right and most of the manufacturing sectors must hire MME students but instead of hiring metallurgy students they are hiring Diploma and mechanical students.

Cheers to your perception. Its good that you shifted your focus from JEE to Masters entrance. Talking about IIEST, an interesting fact about this college is that unlike other colleges, who have their starting rank in CSE or CST, starting rank of IIEST comes from Aerospace department. The reason being the academic excellence of the faculty here. Whether you want to further pursue masters or not, thorough knowledge of your B. Tech. or B. E. syllabus is always advised. You will get an opportunity to complete your bachelors degree under highly influential professors and with some diligence and hard work, you can even prepare for masters entrance without the aid of any coaching institute. And even apart from academics, this institute provides all opportunities for overall development. You will find yourself engaged in managing fests and participating in sports events time to time. So, I would highly recommend this college to you, especially if you want to further pursue your studies for competitive examinations.
All the best for your future.