You need to compare various aspects of both the institutes to reach a fair decision.  The parameters that you should consider for comparing are as follows. 

• Course Structure
• Course Specialization
• Facilities
• Faculty Members
• Placements
• Projects, alumni network, and so on

If you see the course structure and specialization, BHU is the oldest center of study for Metallurgical Engineering hence has loads of data available. But on other hand, less data is available for Material Science at IIT Gandhinagar as it is a growing discipline in the Meta field.

Academics: (Winning Institute - IIT BHU)

1. For IIT BHU, there are two specializations in post-graduation: Alloy Technology and Extractive metallurgy
2. For IIT Gandhinagar, it’s Material Science and Engineering. The course is more focused on Biomaterials and nano-materials.

Here is the list of subjects for Metallurgy at IIT BHU with the first 5 being the core subjects:

1. Metallurgical Thermodynamics and Kinetics
2. Computational Methods for Metallurgy
3. Computer Applications in Metallurgy Practical
4. Materials Characterization
5. Materials Characterization Practical
6. Departmental Elective
7. Humanities/Language

Facilities:

Now coming to the facilities, IIT BHU offers you a long list of facilities for this particular program which are:

• Transmission Electron Microscopy Lab
• Scanning electron microscopy with EBSD Lab
• Projection Microscopy Lab
• Structural Metallography Lab
• Mechanical Testing Lab
• Computer Lab
• Extractive Metallurgy E&C Lab
• Chemical Metallurgy Lab
• Transport Phenomena Lab
• Welding Lab
• Foundry Lab

Faculty:

The faculty at both the institutes are quite good, to know more about the faculty you can visit their official websites:

Placements: 

Now, coming to the placements, both the institutes offer moderate placements in these fields. Most of the students switch to Ph.D. from India as well as in international institutes.

All in all, it depends on your interest and goals. So,  make such decisions carefully. 

One of my cousins recently encountered a similar situation where she had to choose between an M.Sc in Chemistry at BITS Hyderabad, and Biotechnology at NIT Warangal. 

1. Having a conversation with the seniors, she found out that placements at NIT Warangal for Biotechnology, Metallurgy, Civil, and Chemical, are not as good as they should be.
2. The recruiters are a handful, like Dr. Reddy’s, who recruit a few students out of many. Most of the students begin preparing for CAT or GRE during their 3rd and 4th year of the course.
3. The ECE placements are quite reasonable. This means, the median package for circuit branches in BPHC can range anywhere from around 10 LPA to 11 LPA, while the average package can still be higher. 
4. However, Metallurgy will not supposedly bring as many prospects as other branches can. It can pose a real problem in your case. You can choose to pursue an MBA or opt to study abroad for an MS. 
5. But, M.Sc in Biology at BITS Goa can possibly be a good choice because you will still secure a position in EEE, ECE, or ENI. It can fetch you a position in the IT sector. The placements between BITS Pilani and BITS Goa are almost in the same range, with little to no difference at all.
6. Only recently, there are candidates who went abroad to MIT or Caltech after their M.Sc, to pursue their thesis. It can make an easy dodge for you to secure seats in MS or Ph.D. programs.

Thus, going for BITS Goa can be a superior choice to the NIT Warangal. 

A lot is taught about fieldwork when one does their B.Tech. in MSE at IITGN. If you are eager to gain more and more knowledge then it is advisable to take up projects under the professors.

Also, the facilities provided by IITGN are commendable and the college possesses very well-equipped labs. They also have very good types of equipment for research in the field of Material Science.

Therefore, the opportunities after the completion of a degree are enormous. After your graduation, you can move to universities outside India to pursue a Master’s or a Ph.D. degree where your knowledge of B.Tech. would come in handy. Students can also take up jobs in the Steel industry or the Material’s related labs in India.

My friend is currently pursuing B.Tech from NIT Raipur in the mechanical department. His honest opinion says that you should go for metallurgy at NIT Trichy. Here’s why

• If you went for the wrong branch or found out later that this is not your cup of tea, then after the 1st year you will have an option called branch sliding. In this process, you can change your branch from the current one to the desired one based upon the number of vacancies and score.
• If you went for the wrong college, then there's no option as a college slide! You’ll have to devote your 4 years in that college anyhow, except if you again decide to give mains.

So, if you simply want to get into a better place then choose NIT Trichy. This is because you can get the advantage of branch sliding anyhow. However, if you don’t want to take risk of not getting the desired branch, then go for NIT Raipur.

At last, sort your preferences and know your sole aim. Because in the long run, your happiness and satisfaction are what matters the most!

Surely, Metallurgy at PEC over Mechanical in UIET. There are various important reasons behind this: Placements in PEC are better, companies like Google, Amazon, Microsoft, etc. visit campus for placements.

Though metallurgy has fewer placements than other branches in PEC, once you are in PEC and if you are focused enough, you can go for an upgrade after 1st semester on the basis of CGPA. To aim for it, keep the following things in mind -

• At most, only the top 10% of the class can be upgraded.
• The branch you want to be upgraded to will only be available if it has vacant seats.

PEC is far superior to UIET in terms of cultural and other extracurricular activities. If you don't have any branch priorities, I'd recommend metallurgy in PEC.

My brother had the option of VIT for CSE on merit still he chose PEC metallurgy. There are various reasons as to why he took that decision:

• VIT is more expensive. Even if he had gone on merit, it would have cost him much more than PEC.
• Placements in core companies in ECE are negligible. You can sit for IT companies, but they pay less to ECE undergraduates than CSE counterparts.
• If you are a north Indian, culturally VIT might be different and might take time to adjust.
• Metallurgy is an undervalued branch in India; many of my seniors are pursuing MS from Germany, the United States, and France, and some have gone to IIMs and FMS with strong credentials.
• One of our seniors received a PPO of 15 lakhs, which is more than many students from elite branches.
• You can choose to upgrade, but you'll quickly realize that it's not that simple because the grading criteria favors those who are less deserving (no offense).
• Whether you accept it or not, those who claim that placement in metallurgy is poor (as it is in all branches except CS/IT) are correct. Placements in the core are hard to come by.
• Only 4000 people in GATE are from metallurgy, whereas there are 1.8 lakh from CSE and 2.1 lakh from Mechanical, implying that the probability of you getting a PSU is greater than that of a mechanical engineer.

I personally believe VIT is overrated because a friend who did not even pass mains received 2000 AIR in VITEEE. In the CBSE 2016 boards, he scored 78 percent, which was below average.

It depends upon your expectations, your goals, your abilities, etc. The worth of doing Material Sciences and Metallurgy Engineering at PEC Chandigarh will depend on the following factor:

• If you gave your very best at the entrance exams but still could not score well enough to get a higher rank which would have given you an option for a better college or branch, then probably it is best to move on and choose the branch and the college. There will be opportunities here as well, no doubt about that.
• If you think you did not give your full efforts and you could do better in the next year, then definitely you should drop a year for better preparation. It is better to drop rather than lamenting in the future that you did not give your 100% and got stuck here.
• If you prefer engineering and you are passionate about the subject, then the college reputation and brand should not bother you much. It is about the learning you would get and not about other stuff like rankings, placements, etc. You would get plenty of options and opportunities here as well and after graduating too.
• If placements matter to you more than anything and you do not have any preference about the branch you would get, then definitely you should prefer a college with a better reputation, placements, etc.

PEC Chandigarh is not a bad college and has a legacy of close to 100 years now. It is also ranked 68 in the NIRF 2020 engineering college rankings. Take a decision based on what you want rather than superficial stats and other things.