There are different viewpoints for the same question. It primarily depends upon what is best for you, and whether or not the course you are willing to take interests you. 

One of my friends encountered a similar problem likewise, and addressing the same, here are some points you might want to consider before diving into any conclusion,

1. A dual degree in Mathematics, Physics, and Chemistry is claimed as a part of Science, while others are considered in the case of Engineering. You will learn the theories of science instead of the application of technology.
2. In Mathematics, you are supposed to learn the series of higher-order and their respective application. While, in Mechanical Engineering, you will learn more deeply about Engines, Boilers, Automobiles, Refrigerator Systems, and much more.
3. A single degree, like Mechanical Engineering, CSE, EE, Civil Engineering, or Chemical Engineering, can be more advantageous than dual degrees. 
4. If you opt for a dual degree in Mathematics, you have a higher probability of becoming a mathematician or a professor. But, in case you pursue Mechanical Engineering from NIT Surat, then you bear higher chances of securing a placement offer at top-tier MNCs.
5. Your choice should always remain ahead of most others. The one piece of advice is that in NIT Surat, you supposedly cannot change your degree from M.Sc to B.Tech following the 1st year and vice versa. 

You should research the same for BITS Goa and find whether or not the rule is similarly applicable in the institute. This is the basic difference you can find between both institutes. 

Presidency University, Kolkata is a better to place to study economics than BITS, Goa, or Hyderabad. Presidency University, Kolkata is well known for its economics department. It also has an excellent subject record.

In the national ranking too Presidency University comes at the top. One of my cousins studies at Presidency University, Kolkata. And he vouches for the Economics degree provided by the institute.

Taking into consideration various factors like fees, faculty, it is safe to say Pracidency University is the better alternative.

But if you are looking for placement after graduation, then joining Presdancyi will not be a good idea. Although their Economics dept. Is well-renowned, they don’t offer placements after graduation. You will have better placement opportunities at BITS Goa.

First of all, I want to clarify that there is no such branch called CSC in either BITS Pilani or NIT Calicut. Both the colleges have Computer Science & Engineering (CSE) degrees 

• BITS Pilani is a top private engineering university. However the same cannot be said about its Goa campus. 
• NIT is a brand that is recognized instantly by almost everyone in any part of the country and this gives NIT Calicut a distinct advantage. 
• As it is a government-run college the learning environment is also better due to the better quality of students. 
• Companies also prefer NITs over private engineering colleges. You will get better job opportunities at NIT Calicut.

Hence it is suggested that CSE at NIT Calicut is a much better choice than CSE at BITS Pilani Goa campus.

BITS Pilani is the number 1 private engineering college in India and is one of the largest engineering colleges in Dubai. Manipal University Dubai attracts over 1500 students all over the world and has a campus that stretches over 75 acres.

Course Details:

BITS Pilani:

• It offers B.E.(Hons) in Computer Science and provides its students with an updated and industry-related curriculum.

• The CS department of BITS Pilani is in association with the MSDN and hence students are free to use the most advanced and updated tools.

• There are currently 350 students and 10 faculty members in the C.S. department. BITS Pilani has faculties from reputed institutions like IITs, IISc, and its sister branches in India, all of whom have a Ph.D. or are in the process of getting one.

Manipal University:

The university offers BTech in Computer Science, and here too the course curriculum is in tune with the current needs of the industry. The labs and classrooms are of top quality as well.

Admission:

BITS Pilani:

• Students must score 60% in Physics, Chemistry, and Mathematics combined and 50% in each subject in their 10+2 in order to seek admission.

• Students must have 61 points in TOEFL and 5.0 in IELTS (not required if the student is from English medium school).

Manipal University:

• Students must secure 50% in Physics, Math, English, and Chemistry/ Biology.

• IELTS scores are accepted but not mandatory.

Tuition Fees:

The annual tuition and fee for the first year at the two institutes are given below.

Scholarships:

BITS Pilani:

There are numerous scholarships offered by BITS Pilani, all of which are merit-based.

• The Tuition fee scholarship provides a maximum amount of INR 1.73 lakhs per student.

• BITSAT scholarship provides a maximum amount of 3.2 lakhs per student.

Manipal University:

• Manipal University offers merit-based scholarships based on the percentage obtained in the 10+2 examination.

• The university also provides sports scholarships.

Placements:

• Companies like L&T, Hellmann, Emirates, and Lamprell visit Manipal Dubai for placement.

• Companies like Zomato, L&T, Schneider Electric and Siemens come to BITS Pilani for recruitment.

Both colleges were established around the same time. Both colleges being two of the leading private colleges in India, their growth has been almost the same. So, choose the institute according to your convenience.

ICT (Institute of Chemical Technology), Mumbai has received ‘A++’ accreditation by NAAC. In the current year 2020, ICT (Institute of Chemical Technology), Mumbai has been ranked by the NIRF at 18 for its Engineering degree course offered. BITS Pilani (Birla Institute of Science and Technology), Goa has been accredited ‘A’ grade by NAAC and is duly recognized by the UGC, offering degree programs at undergraduate as well as postgraduate level in the field of science and technology.

Admission:

Textile degree in ICT (Institute of Chemical Technology), Mumbai:

• The candidate opting for a Textile degree in ICT (Institute of Chemical Technology), Mumbai is selected on the basis of entrance examination of GATE, GPAT.

• The total fees for the Textile degree in ICT (Institute of Chemical Technology), Mumbai is INR 1.53 Lacs.

MSc Maths at BITS Pilani (Birla Institute of Science and Technology), Goa:

• The candidate opting for MSc Maths at BITS Pilani (Birla Institute of Science and Technology), Goa is selected on the basis of the entrance examination of BITSAT.

• The total fees for MSc Maths at BITS Pilani (Birla Institute of Science and Technology), Goa is INR 4.13 Lacs.

Placements:

Textile degree in ICT (Institute of Chemical Technology), Mumbai:

• The top recruiting companies visiting the campus of ICT (Institute of Chemical Technology), Mumbai to offer placements to the graduates in the field of Textile are Tata Motors, Reliance, Johnson Johnson, Nerolac, Jacobs, ITC, Exxon, Cipla, Asian Paints.

• The average annual graduate salary offered for placement is INR 4.8 Lacs.

MSc Maths at BITS Pilani (Birla Institute of Science and Technology), Goa:

• The top recruiting companies visiting the campus of ICT (Institute of Chemical Technology), Mumbai to offer placements to the graduates in the field of Maths are Bajaj Auto, Adobe, Oyo, Morgan Stanley, Uber, Dell. IBM, Flipkart, Genpact, Wipro, Intel, Cognizant, Amazon.

• The average annual graduate salary offered for placement is INR 6.15 Lacs.

Both courses have their advantages and disadvantages. These are some of the key information about the two courses. Go through them and decide which will be better for you.

The preference is always given to BITS Goa as it belongs to the most reputed family of BITS institute. One of my friends has studied there and he loves the campus from all aspects.

The major reasons as to why BITS Goa is to be preferred are:

Scope

• CSE has more job opportunities in the market as compared to other branches of engineering. 
• If you even go for a core organization in the chemical field; the highest package is not more than 6 LPA. 
• In the case of CSE, if you are into coding a good package can be cracked.
• The highest package is close to 1.40 crore in BITS Goa. The average also stands at a decent place. 
• The prominent recruiters are - ADM Argo, Adobe, Bajaj Auto, Capgemini, CGI, Cisco, DE Shaw, EXL Services, Razor Pay, Reliance Jio, Freshworks and Goldman Sachs.

Faculty

• The computer science faculty cannot be compared with chemical engineering. 
• CS faculty is amazing having well-equipped knowledge in the field to deal with real competition. They all are efficient in imparting real practical skill set to their students in a proper manner.

Campus

• Goa is a place people look out for holidays, and having a college in Goa makes it even more fascinating and attractive. 
• Certain limitations are also imposed on students. You cannot leave the campus before 5 PM and you should return back by 11 PM. 

BITS Goa makes it a better option on all fronts whether its faculty, campus, or scope. Having this outlook will help you get to a good institute. The stream can be a point of interest but other factors also matter.