BITS Pilani is better. In terms of academics, infrastructure, alumni base, job roles offered, placements, start-up culture, peer group, academic flexibility, and freedom provided, it is well ahead of NIT Surathkal. The BITS Pilani name has better national and international recognition. In terms of placements, it ranks right after the top 5 IITs. 

BITS Pilani placements 2022 witnessed an average CTC of INR 28.99 LPA. The highest CTC offered this year was INR 1.33 CPA. Microsoft, De Shaw, Flipkart, Amazon, etc. took part in the placement drive. 

You should choose BITS Hyderabad/Goa. BITS Goa CSE is considered to be on the same level as the Pilani campus. The Hyderabad campus has made some radical improvements over the last few years, as well. Due to the presence of Hyderabad IT hub, the placement and career opportunities available are ample. 

BITS offers a lot of freedom to students. Their no-attendance rule and the flexible course structure allow students to explore and take different courses according to their interests. You can leverage these benefits to shape your career, the way you want. 

BITS placements are comparable to old IITs. Almost all major recruiting companies that visit IITs, visit BITS as well. 

Applied Maths at IIT Roorkee is a more viable alternative than BITS Goa CS provided that you have an interest in coding. 

• The course structure of Applied Mathematics is quite similar to that of KGP MnC. Unlike the general assumption, this program isn’t research-oriented. Only a few who have a deep passion for Maths take up research as a much later endeavor.
• The best part of the program is the excellent job opportunities it offers. Its placements are second only to CS, the most preferred branch.
• You get to avail top-notch facilities provided by a leading IIT, Roorkee
• IIT Roorkee has the highest intake of this program even more than IIIT Hyderabad.
• The Applied Maths team bagged the 68th position in the ACM ICPC world Finals and the 2nd position in India.
• The course structure covers diverse topics like data structures, design, Analysis of algorithms, and discrete mathematics. All these topics help to strengthen the Computer programming base of students.

So, Applied Mathematics is a much better option than BITS Goa CS.

The job opportunities in both Chemical and Civil are very limited and it’s also difficult to switch domains later. The core opportunities consist of more of a blue collared job. One can go for Government jobs if interested.

Go for CS in BITS Goa if you are looking for excellent placement opportunities or higher education. CS provides excellent opportunities in terms of higher studies and research work. But if you are adamant about Civil or Chemical, go only if you are genuinely interested, and that too after in-depth research about the nature of work.

The only drawback of joining BITS Goa is the exorbitant fees which might be a major issue for many. Apart from this the branch is very promising and is expected to grow more so. It’s recommended to contact working professionals in the field once and enquire about career prospects. Also, go for CS only after gaining a basic level of coding skills.

If you look at a general perspective, both IIT and BITS are extremely prestigious Engineering institutes in the country. Both have managed to contribute largely to the world's technological map. IIT JEE is the national-level exam for Class 12 students for admission to IITs while the entrance exam to BITS is the only engineering entrance exam in India to evaluate candidates on the basis of Logical Reasoning and English language skills as well.

I have drawn a general comparison between the 2 institutes on the basis of some common aspects

Entrepreneurs: The success of an Engineering institute depends primarily on its Entrepreneurship culture. Some Famous entrepreneurs from both institutes are as follows 

IIT Entrepreneurs:

• Dipchand Deep Nishar was the highest-paid manager at LinkedIn till 2014. Currently, he is a board member of TripAdvisor and a software company called Opower and also works as an advisor for several tech companies.
• Nikesh Arora, a graduate of IIT-BHU, is one of the highest-paid employees at Google. He is the Chief Business Officer and a Senior Vice President in the company.
• Soumitra Dutta from IIT-Delhi is the Dean of Cornell University’s Management School.
• Vinod Khosla from IIT-Delhi again is the co-founder of Sun Microsystems. 

BITS Entrepreneurs

• Baba Kalyani is the Chairman of Bharat Forge.
• Prithviraj Chavan is the Chief Minister of Maharashtra.
• Rakesh Kapoor is the CEO of Reckitt Benckiser.
• Sanjay Mehrotra is the President and Co-founder of SanDisk.
• Sunil Duggal is the C

Placements 

We can safely conclude that placement scenario at IIT Bombay is better than BITS.

Campus life: BITS Pilani has a better campus life and culture than IIT Bombay. It boasts of a well-planned campus, libraries and hostel facilities. It has a unique concept wherein students take tutorials from their various teachers. Its cultural event Grubs is quite popular in engineering students.

Fees: IIT Bombay Total fee is around INR 9,50,000 (BTech) whereas BITS semester-wise fees is 2,31,500/-

Since IITs are run by the government, studying at IIT is cost-effective whereas BITS are expensive.

Infrastructure: Both IIT campuses and BITS Pilani campuses have top notch infrastructure. However, most of the new IITs lack a permanent campus and are also facing a lack of a good faculty positions. BITS has a limited number of campuses that are well-established and it is known to upgrade its world-class infrastructure on a regular basis keeping up with changes in technology.

Faculty: BITS Pilani attracts the best faculty from India and abroad. It offers better salary and more freedom to its teaching staff. Whereas IITs often face faculty issues. Many new IITs depend on guest faculty or visiting faculty to conduct their classes.

I would suggest you to choose IIT mainly because of low fees and the IIT tag.

First of all, neither ACM-ICPC nor GSoc truly defines a person's worth or skills. I have seen many IITians mocking GSOC claiming it to be worthless. The truth is quite different. GSoc is one of the best opportunities for 1st and 2nd years, and for anyone not interning at Google, Microsoft Research, Stanford, ETHZ, and similar companies. However, GSOC required a lot of dedication and commitment. IITians prefer easy jobs that require minimal effort. This is the reason they prefer foreign internships that can be easily sought because of the IIT tag. 

GSOC belongs to an altogether different league. You have to spend months contributing bug fixes to a project and staying dedicated over a long time. Your school name has no value unless you work hard to demonstrate your dedication.

GSOC is worth a lot and IITians are usually misguided by their seniors to believe the contrary. One gets to design a good project proposal, compete with everyone from all over the world and then implement it. This is way better than the web application development one does at Goldman or Morgan or Yahoo. 

Usually, institutes like BITS Goa and IIIT-H are only after success and thus try to compete with the big names to gain fame. So it’s better if people with privileged backgrounds and institutes make their names for themselves and stop dominating those that have earned their worth through efforts and not just tags from big institutes.