If you are concerned about the brand then definitely go for IIIT Allahabad. But, if you are clear with your choice of stream you can choose either of them. If you choose NIT Jamshedpur CSE it’s good and so is the same with IIIT Allahabad. 

I can share one of my cousin’s experiences, who passed out from NIT Jamshedpur.

• When he cracked the JEE with decent marks and got a chance to opt between these two colleges; he chose NIT Jamshedpur CSE over IIIT Allahabad comparing few factors like placements, exposure and money plays a vital role here.
• It is all up to you whether you want a tough competitive exposure or a light and cooperative environment.

Let me make it more clearly for you by categorizing engineering colleges:

This categorization might help you to decide. Also, skills do not depend on the branding of the building. It is something you learn eventually. Moreover, choose a college which has easy access to transport, shops, etc.

Also, if you see around there is infinite demand for highly skilled electronics engineers with impressive TopCOder and GitHub profiles. So, choosing either of the colleges won’t be a loss. But, if you have a specific interest in a particular stream like ECE in IIIT Allahabad or NIT Jamshedpur will prove a good choice too.

A relative of mine who is an alumnus of NIT Jamshedpur and she has said that the institute is working on its boundaries to make them close. You can easily get into the premises of the institute. Even the locals do.

You will have to clear JEE to get into the Bachelors in technology. If you clear your GATE exams, you can get into M.Tech, PhD, and M.Sc. After you clear interviews, you can get jobs of technician, site engineer, etc.

Some requirements for admission are as follows:

• Clear your JEE
• Get a decent rank
• Clear your CSAB JEE counseling
• Fill choices, and make sure you have NIT Jamshedpur as your first priority. Pay your fee and get a payslip.
• Produce required documents at NIT Jamshedpur and the fee slip.

It can be seen that JEE is very important for getting admission to NIT Jamshedpur. So clearing that exam with a decent rank is important.

You are comparing two different engineering branches which are core and are perfect in their own place. Also, the selection of the branch should be primarily based on your interest and future plans. It is very important you choose a branch of your interest, as you will spend 4 years learning it. So, decide on the basis of your interest.

NIT Jamshedpur is much better than BIT Mesra in placements except CSE. CSE has slightly better placement in BIT Mesra than NIT Jamshedpur but then the gap is decreasing year by year. So, you can easily opt for the choice of field you want.

Let me give you some details regarding the future prospects in both of them:

Core Jobs:

• Both the branches have an equal number of core jobs and both mechanical and electrical engineers are needed at any manufacturing firm.
• So in this case, it primarily boils down to your inclination towards either of the two branches.

Non-Core Jobs:

• Electrical Engineers also have the opportunity to switch their career to software engineering without much difficulty.
• Mechanical Engineers generally don't have this Liberty.

Government Jobs:

• Mechanical Engineering has the highest no. of vacancies in PSUs and Engineering services.

Several core companies come to campus at Jamshedpur in TATA town, TATA Powers and TATA Motors pick many students for jobs as well as for internships. Now, this brings a great advantage for both Mechanical as well as Electrical branch students.

Talking about infrastructure, BIT Mesra has a more beautiful campus than NIT Jamshedpur. If you want facilities, you should go with BIT Mesra. But, placement wise NIT Jamshedpur is far ahead of BIT Mesra, which is again proving NIT Jamshedpur worth over bit Mesra.

Based on the above parameters, you can decide for yourself. Regarding the two colleges you mentioned, both are equally good and have roughly the same student quality. BIT Mesra has an edge in software profiles and NIT Jamshedpur in Core Engineering placements.

ECE in NIT Jamshedpur would be a better option than IT in BIT Mesra considering the facts given below. One of my friends pursued her ECE degree from NIT Jamshedpur and had a good experience. 

Placements: (Winning Institution - NIT Jamshedpur)

• The placements in NIT Jamshedpur for the ECE branch are much better than IT placements in BIT Mesra. 
• Most of the students of NIT Jamshedpur get placed in the software companies, only a few core ECE companies visit the campus.

Infrastructure and Faculty: 

• The college infrastructure and faculty of NIT Jamshedpur are not very up to the mark but then you cannot depend on the teachings. 
• Most of the time you have to study on your own or along with your friends. 

Branch Selection: If you are interested in opting for the IT branch then you can definitely go for BIT Mesra but if you have certain confusion in your branch selection, then it is recommended to choose ECE from NIT Jamshedpur. 

Mess and Hostel: (Winning Institution - NIT Jamshedpur)

• NIT Jamshedpur takes really good care of its students. Facilities like hostels and mess are really awesome. From the tasty food of mess to the clean rooms of the hostel, everything is just perfect. 
• My friend visited BIT Mesra for a workshop and according to her experience, the food at the campus is not that good. Their facilities are not up to the mark. 

The following tables have a comparison of the BIT Mesra and NIT Jamshedpur.

Considering all the facts mentioned above, NIT Jamshedpur stands out to be the better option.