Both Metallurgy at NIT Warangal and MSc in Biology at BITS Goa are great programs offering a plethora of opportunities and exposure to its students. But the choice between the two is a very personal matter as both the branches are very diverse in the opportunities they offer. So

• Go for NIT Warangal if you are interested in Metallurgy
• Go for BITS Goa if you are ready to Study Biology along with BE Degree.

However, you need to bear in mind the fact that BITS Goa is expensive and the fees is very high around 25 lakhs while NIT Warangal's total fees are less than 10 Lakhs.

I would like you to consider certain important things before making your decision-

• College- Without a doubt, NIT Warangal is ahead of NIT Durgapur in terms of faculty, infrastructure and hostel facilities.

• Subject - You need to choose your subject based on your interests. Without that you’ll either hate your profession or choose a completely different career path altogether. If you are into math, coding, logic and problem-solving, choose CSE. On the other hand, if you want to study materials, metals, extraction, etc, choose Metallurgy. 
• Profession - CSE will give you better opportunities in the IT sector. You might get a fat check, work for a good company, and live in metropolitans. As you know, IT jobs are basically office jobs.On the other hand, core Metallurgy jobs deal with steel plants, mines and such. You’ll end up working in a remote area if you choose a core job.The placements for CSE are overall much better than Metallurgy, across all engineering colleges. But if you have a passion for metallurgy, you might end up in a good brand or get selected for a government position. 
• Location- Both the places are culturally very different. Research a bit, and figure out which place’s food habits, climate, and culture suits you better.

According to me your college will last for 4 years. However, your branch will become an intrinsic part of your personality and profession. Unless you have an interest in Metallurgy or a good chance at sliding to another branch, choose CSE at NIT Durgapur.

I think the branch matters more than the institute and that being said personally I feel IIT Bhilai Electrical is a better option than IIT Indore Material Science. The small batch size enables you to make the most out of the opportunities and resources. The points below further prove my opinion 

Here is a small list of things why you should consider IIT Bhilai:

• The professors come from IIT Hyderabad, one of the most reputed and well-regarded new IITs.
• The fractal system is followed here giving you a more flexible academic palette. 
• The core subjects are introduced in the first semester itself so that students can identify their interests early. 
• IIT Bhilai EE lab is one of the very few labs in India which is Cloud Connected.
• There are 20 All-in-ones that have 8-core i7 processors in the EE lab.
• The institute has vibrant campus life with dynamic student activities going on such as 6 cultural clubs and 3 tech clubs.
• The Electronics Club of IIT Bhilai Is well-equipped and enables you to experiment with various modules like GPS module, GPRS module, accelerometer, etc

Overall, taking IIT Bhilai will not disappoint you and you will have a plethora of opportunities here.

IIT Roorkee, NIT Trichy, and NIT Warangal are well-established institutes in India. The scope of metallurgy is comparatively lower than that of CSE. IIT Roorkee mainly concentrates on textual learning and does not give the students exposure to practical learning. They are using the practice of mugging up the lessons without having a clear understanding of the topic. The placement is very poor here; the students from the metallurgy department usually end up in data analytics and coding.

So CSE at NIT Warangal and Trichy would be a better choice.