What should I take, Metallurgy and Material Science Engineering at IIT Indore or Electrical Engineering at IIT Bhilai?

In general, it is better to choose the branch of your choice. Given below are a few trade-offs of the two choices given on the question which may help you in making the decision. 

MEMS - IIT Indore:

• Administration: IIT Indore belongs to the 2008-09 batch of IITs. Although it can’t be compared with older IITs but it has made remarkable progress in this short span of time. The administration and departments are well-settled. Extra-curricular at the institute are also developing with time. In 4-5 years, the institute is expected to have a great future.
• Course: BTech MEMS at IIT Indore is fairly new and the duration of the existence of the course is the same as the B Tech Electrical course at IIT Bhilai. However, the MEMS department has been functioning for a while at IIT Indore. As a department it has experience. The faculties are great. 
• Placements: MEMS has a lower placement rate as compared to other core branches of engineering. Metallurgy and Material Science is a niche field of study and the degree outcome is more research-oriented. 
• Change of Branch: However, you can change your branch to Electrical or Mechanical from MEMES at IIT I, if you work hard in your 1st year. Changing to CS is always difficult because of the competition.

Electrical at IIT Bhilai:

• Facilities: IIT Bhilai was established back in 2016. It is only 4 years old. Electrical is a core Engineering discipline with better career prospects. But the disadvantage of this choice is the institute. You will have a few seniors in your branch and temporary faculties.
• Extracurricular: You will have good opportunities to start events, clubs, in the institute. On the other hand, the future at this institute is a bit uncertain.
• Campus Life: The institute also does not have a proper campus. You will not have a proper campus life for the next 4 years. 

The table below shows a brief overview of the two institutes.

One of my friends had an option between Mechanical at IIT Indore and CS at a new IIT. He chose Mechanical at IIT Indore. Judging by his experience it is safe to say that he made the right decision at least for 2-3 more years. 

The choice is up to you if you would rather trade off on the branch or on the institution. If you are confident you can secure a good future from the limited opportunities a new IIT can offer, you should go for it.