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.

An ECE at IIIT, Allahabad is preferable to an IT at BIT, Mesra. Of course, the choice of the branch is subjective and should be chosen based on our own interests and preferences. But still, a degree at IIIT Allahabad is much more valuable than that of BIT Mesra.

The best thing about IIIT, Allahabad is its focus on research and thus will provide you the extra edge over other similar level candidates. The course structure is very focused and you will get subjects such as integrated robotics and many others. IIIT, Allahabad also offers the best facilities to hone your programming skills.

The table below will give a few stats of both the institutes.

And then the fee structure of IIIT Allahabad is also much more affordable, 1.65 lakhs first-year fee to BIT Mesra’s 2.85 lakhs first-year fee, compared to BIT Mesra which gives the degree much more value with all the facilities, research opportunities, and placements it has to offer. Thus IIIT Allahabad is favored.

Among the colleges mentioned, the major competition lies between BIT Mesra and IIIT Lucknow. However, this can be compared and proved by the kind of students that take admission in those two colleges in comparison to LNMIIT.

Following are some of the pointers that will give an unbiased review of both the colleges :

IIIT Lucknow

1. You will come across an outstanding coding culture.
2. Its perfect location, located in its city is a major advantage.
3. Its average package is quite comparable to other IITs too in a very shorter duration of time.
4. It holds better fame than other IIITs.
5. You will experience a wide diversity in culture whether it's related to skills or belongings of students.
6. You will have more freedom.
7. You will come out as an important asset for the country for sure.

BIT Mesra

1. You will get access to better infrastructure.
2. You will experience better campus life.
3. You will get a stronger connection to the alumni network.
4. It holds a bigger campus area.
5. Its reputation is top out of other IIITs.

In conclusion, IIIT Lucknow’s progress is many times faster than BIT Mesra. Even the B.Tech course in Computer Science at Indian Institute of Information Technology, Lucknow has the lowest fees than the other two colleges.

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.