I have friends pursuing courses you mentioned above at either institute. Based on the discussion I have with them, here is what should be best for you,

1. The institutes can be considered quite equivalent to one another, but BITS Goa has an upper hand. 
2. M.Sc at BITS Goa can be specialized following the first year, during which you will be allocated a B.E course depending upon your CGPA. 
3. With a 6 CGPA, you can get Mechanical Engineering, which is quite an easy job. In contrast, it is better than ICE.
4. However, if your scores are high enough then you might get a seat in CSE. 
5. By the end of 5 years, you will be receiving a B.E and an M.Sc degree, which is nonetheless a smarter choice. 

However, the fees at BITS Goa are quite a lot. 

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. 

Indira Gandhi National Open University is the only university that provides open, distance, and online modes of learning in the country. It basically has extended its affiliation to 21 schools.

It is known as People’s University as it provides access to higher education to all segments of society. The university offers a network of 56 regional centers, 11 recognized regional centers, and approximately 2000 support centers across the country. It offers 21 different school education to its individuals across the country.

The MSC course is provided in 3 different streams. It is also provided in Mathematics with Computer Science. The other details are described below.

Admission:

• It is a distance course with a minimum duration of 2 years and a maximum of 4 years.

• The fees for students in the general category stand at Rs. 33,600 while for the scheduled caste category it is Rs. Rs. 26,400.

Eligibility:

• The mandatory criterion stands around being a graduate with Honours in Mathematics. The minimum score should be at least 50%.

• BA/BS.C. degree is also acceptable with mathematics one of three main subjects.

Program Structure:

• The course curriculum consists of both core and elective courses.

• The program follows the credit system, providing credits at the completion of different elements.

• The credits distribution can be divided into three parts, i.e. Core courses- 34 credits, Elective Courses- 26 credits, Projects- 4 credits

• Core courses are taught during the first two semesters to gain hands-on knowledge of the subject.

• Elective courses are more inclined towards the application of mathematical sciences.

Program Resources:

• The university provides study material in various formats to the students due to the distance pattern of examinations.

• It can include self-instructional print material, wrap-around material, assignments, counseling sessions, projects, and practical work.

• The print material is provided to candidates through the post to access detailed mechanisms.

On the whole, the entire program is designed to make learners properly trained with the core mathematicaladmi knowledge. The fee range is also not very high making it an advantage plus a distance course is always preferable if you are doing a job or pursuing some other regular courses from any institute.

The Joint MSc Ph.D. Mathematics program at IIT Bhubaneswar is pretty good, in fact, it is one of the very few IIT that delivers this specific program. From the academic year, 2013-14 IIT Bhubaneswar is offering this program. You can take admission through a valid score in JAM. The minimum educational qualification required for this program is a bachelor’s degree with Mathematics / Statistics as a subject for at least two years/ four semesters. There are in total 20 seats available for this specific program.

Any student admitted to a Joint M.Sc.-Ph.D. are eligible for consideration to take admission into Ph.D. programs provided the student obtains a certain minimum CGPA at the end of the fourth semester. Otherwise, the student will have to leave with an M.Sc. degree. One can also on their own, decide not to continue with the Ph.D. program and leave with an M.Sc. degree after successful completion of all the academic requirements for the first four semesters.

The School of Basic Sciences in Bhubaneswar has good and experienced faculty members. It has received various research and consultancy projects funded by agencies like DST, CSIR, DBT, BRNS, as well as industries. The research focus for Mathematics at this IIT is mostly on, Optimization Techniques, Transport Phenomena & Molecular Dynamics, Queuing Theory, Applied Probability Models, Biomolecular Transport Dynamics, Soft Computing, Computational Fluid Dynamics, Numerical Methods, Combinatorial Matrix Theory, Graph Theory, Complex Dynamics, Fractals, etc.

Although IIT Bhubaneswar is among the new IITs, it holds a good placement record. According to 2019 placement highlights, the average salary package offered at this IIT was 11.44 lakh per annum. And a total of 89 companies visited for recruitment last year. 

So, if you want to pursue Joint MSc PhD Mathematics, IIT Bhubaneswar is definitely a good option.