There are many aspects to this answer. If you are from South India then go for NIT Calicut. It has a reputation for good placement records. Here are the placement statistics for both NIT Calicut and VNIT Nagpur.

If you are not from South India, then choose according to your convenience. Don’t choose Calicut over Nagpur as it is not an easy place to live in for four years. If you like a lot of alone time then Calicut will be suitable for you. Nagpur is in central India. So, you will have easy connectivity to your home town. VNIT is located in the middle of the city. You will enjoy your stay there. 

Both are good institutes. Choose according to the proximity.

NIT Surathkal is ranked 13 in India for BTech by NIRF 2020. Whereas, NIT Nagpur is ranked 27 for the same by NIRF 2020. NIT Nagpur also ranks 3rd in Maharashtra by NIRF 2020 and has collaborated with many industries and R&D organizations.

As the courses in the question are not the same it is tough to evaluate which institute will be better. Here is some of the important information about the two courses which may help you in making the decision. 

Admission:

NIT Surathkal:

The mechanical department at NIT Surathkal has produced over 4500 mechanical engineers graduates across the nation. It offers a BTech program for Mechanical.

• The essential eligibility criteria for admission is 10+2 in the science stream, with a minimum of 75% aggregate. 
• The candidates’ selection is based on the JEE Main score, and the seats are allocated through JoSAA counseling.

NIT Nagpur:

CS department at NIT Nagpur has well-qualified, motivated support staff and faculty members.

• Admission to the BTech CS program at the institute is based on the marks obtained in JEE Main. 
• The final selection is based on the JoSAA counseling round. 

Placements:

• The placement average for NIT Surathkal is 100%, whereas at NIT Nagpur the placement rate is 85%.
• The highest CTC received by the students of NIT Surathkal is INR 39 LPA. The highest CTC offered at NIT Nagpur was 52 LPA.
• The top recruiters for mechanical at NIT Surathkal are Tata Group, Godrej, L&T, Thermax, Google, Microsoft, Apple, Ashok Leyland, General Motors, etc.
• The top recruiters for CS at NIT Nagpur are Goldman Sachs, JP Morgan, Infosys, Dell, Deloitte, Capgemini, Thermax, ZS Associates, etc.

In terms of industry trends, CSE is in more demand than Mechanical engineering. Both the NITs are reputed and offer decent academics along with good placement opportunities. However, you should choose the stream in which you are more interested.

NIT Warangal is ranked 19 for Engineering by NIRF 2020. Whereas, Manipal University is ranked 54th for Engineering by India Today 2020. There are various programs offered in UG, PG levels by these two engineering colleges. They also offer Ph.D. degrees. The popular programs offered by Manipal University and NIT Warangal are B.Tech, B.Sc, BBA, M.Tech, MSc, MCA, and MBA. NIT Warangal currently has 13 academic departments where the Manipal university also has more than 10 departments.

Infrastructure:

The infrastructure of NITW is better than MU. They have a mega Computer lab, game complex, fully equipped laboratories, auditorium. All the departments of NITW are facilitated with LAN and WiFi internet connection and digital classrooms.

Hostel:

NIT Warangal provides better hostel facilities as compared to Manipal university, 23 hostel boards for boys, and 2 hostels for girls. All the rooms are either single and double-seated with air conditioning facilities whereas, at Manipal University, the campus provides the accommodation with more than 220 students along with the required facilities for both boys and girls.

Placement: For placement at both institutes, candidates are selected by companies based on their performance in the Aptitude test, Group discussion, and Personal interview.

• About 150-180 companies visit every year. 80% of the students get placement including all the departments of NITW. The students are getting the highest salary package up to 39 per annum and the average salary package is 9 LPA.

• MU provides an average CTC of 5-6 lakhs per annum. The highest CTC received by the students is 42 LPA.

Recruiters:

NIT Warangal-

Microsoft, Dell, Google India, Amazon, HP, Infosys, Cognizant, Tech Mahindra, Wipro, and many more visit the campus placements.

Manipal university-

Ericsson, Dell, JP Morgan, L & T infotech, Infosys, Cognizant, Microsoft, Siemens, etc. are among the top recruiters at Manipal.

In terms of academics and placements, NIT Warangal is way better than Manipal University. It also offers the NIT tag which is recognized globally. The NITs are well-known for research, training programs, and industrial connections.