Well, it depends upon several factors. A few of them are as mentioned below.

• Where you possibly imagine yourself in the next 10 years and more?
• What has been the real motivation behind your aim for pursuing engineering? 
• What is the time period you are willing to assign for reaching your goal?

There are other factors, or possible scenarios, such as,

• Cushy CTC: In this case, CSE will be better than Mechanical Engineering.
• Higher studies abroad: CSE and Mech both will offer similar opportunities. 
• Competitive examination: In case you would want to take the UPSC examination, IES, PSU, or several others, choosing Mechanical will be better as compared to CSE.
• MBA from IIM: With regard to that, being a student from the mechanical department can give you an edge. As it will offer you diversity points. If however, your scores are low, then you will lose the edge.
• Work destination: If you want to work in Gulf in the future, then choosing Mech is better. If you dream of working in the US, CSE offers better options. 
• If you have a natural affinity towards automobiles then go for Mechanical Engineering. 

The above scenarios can give you possible average outcomes, but there can be vague contradictions as well. You also need to consider which subject interests you. 

According to various student reviews, the preference order for CSE and Mechanical is MNNIT > NITJ. You should always give preference to the branch rather than the institute. Hope this clarifies most of your doubts.

Firstly, you should know that there is no difference in the facilities and reputation of the colleges, Although BITS ranks better as an engineering school. BITS Pilani ranks #30 on NIRF's Engineering rank list and IIIT Allahabad ranks #103 on the same. But you should focus on your monetary capacity in consonance with your future plans before applying. 

My cousin studied at IIIT A and the following points are based on his experience:

• IIIT A is an excellent place to study coding. The classes are good although the syllabus has to be maneuvered because it's tough. You can manage it through attention in the classroom.
• Attendance is an important part of the academic process here because IIIT A has a 75% mandatory attendance rule.
• Without a doubt, BITS has a higher fee range as compared to IIIT A, about 7 LPA for a 4-year program.

Here's a table comparing both institutes:

Lastly, if you love the mechanical stream and are truly motivated to study Maths and Physics then you must go for it. Mechanical is a vast field as well because you'd learn everything related to mechanical processes and even production scheduling. So clearly check your interests and goals before deciding.

Sharda University has been awarded the best private university continuously over the years by National Education Awards. It has also been awarded the best Private Global University of the Year and the Best Innovative Engineering School in North.

Mechanical engineering is one of the most sought after courses at Sharda University. The institute offers a BTech course for Mechanical Engineering. It focuses on the practical understanding of engineering and related concepts and expects students to implore into their syllabus topics and go beyond them. It also aims to allow students to grow through cross-functional activities and networking with companies.

Curriculum:

The ME department aims at providing an industry-centric curriculum and provides a blend of classroom and experiential learning. They include lab exercises, assignments, case studies, and work-integrated activities.

Admission:

• Matriculation with-60% marks, 10+2 with 70% aggregate & minimum 60% marks in PCM, Computer Science/PCB for Biotechnology without a gap between 10th and 12th is the prerequisite for admission.

• Students can appear for the Sharda University Admission Test (SUAT) if they have scored above 50% marks in Maths in 12th Boards to get selected for admission.

• All students up to JEE rank of 3 lakhs and students with UPSEE All India rank up to 50,000 are also eligible for admission.

Placements:

Sharda University has an excellent track record of 91% and 100% placements over the year.

• The highest salary package was 64 LPA.

• Every year about 350 employers recruit students through campus recruitments. Some famous recruiting companies include Amazon, iGate, Wipro, Edelweiss, ITC, L&T, Audi, Asian Paints, etc.

The department provides compulsory internships in the final year and for students who perform exceedingly well get the opportunity to participate in a full-time summer internship in USA, Germany, Mexico and Australia. They also give regular industry visits.