This answer can be answered in 2 aspects; branch wise and Institute wise.
Branch-wise, ECE is way ahead of Manufacturing Science and Engineering and has a wider scope after graduation. ECE students are hired by both electronics and software companies. Moreover, ECE is a major stream whereas Manufacturing is just a sub-stream under Mechanical Engineering.
Specifically talking about colleges only, I would suggest you choose IIT KGP which has a stronger brand name and legacy than BITS Pilani Hyderabad. Its reputation is not just limited to India and has great scope outside India as well. It gets better and more companies than BITS during campus placements.
One major point of difference is the location of both institutes. Hyderabad has a much superior location than IIT Kharagpur thus offering better college life and exposure. IIT KGP is remotely located and lacks the necessary industry touch and exposure.
You have to travel long distances just to eat or do shopping. You will miss out on city life and the opportunities it has to offer. While the campus is great, you have to stay inside as the world outside is desolate. Spending 4 years without much exposure might limit your opportunities.
Hyderabad on the other hand has everything city life has to offer apart from being a major IT hub. This makes it possible to apply for campus jobs as well which is not possible in the case of IIT KGP.
In the end, it’s you who has to make a decision. Go where your heart is inclined the most be it ECE or Manufacturing at IIT or BITS. Just make sure to make a decision that will not make you regret it later.
Many intellectually nourished individuals in both teaching and studying have attended Anna University's College of Engineering, Guindy. The College of Engineering, Guindy, is known affectionately as "CEG" and is surrounded on its campus by neighboring institutions such as the ACT, SAP, and Madras University.
CEG offers a variety of UG and PG courses, as well as B.E-Manufacturing Engineering (B.E-Manu), which is led by the Department of Manufacturing Engineering (DoME) in collaboration with the Department of Mechanical Engineering.
DoME has its own building where classes for UG, PG, and other research scholars are held, as well as labs with both historical and cutting-edge equipment. They also share labs in the Mechanical Engineering Department. The faculty members are highly qualified professionals who have excelled in their fields of study. It has a student committee that organizes two symposiums, one intra-college, and one inter-college National meet, with the committee being guided by a faculty member and all organizational work being handled by students from all four years. Aside from the two conferences mentioned above, other conferences on the advancement of technologies in the field are held on a weekly or monthly basis and hosted by various internationally acclaimed professionals in the field.