BIT Mesra offers 2 undergraduate and 1 postgraduate program in chemical engineering; BE in Chemical Engineering, BE in Chemical Engineering (Plastics and Polymer), and ME in Chemical Engineering.

• If we look at the overall chemical engineering ecosystem in India, it is not very good. There are very few private chemical companies in India. 
• The curriculum of the programs is very old and has not been updated to meet the 21st-century demands. 
• Thus the engineers being produced by the colleges in India are also below par. 
• Close to 95% of the chemical engineering graduates from tier-3 engineering colleges work in service companies with an annual salary of 2-3 lakhs. 

The recent placement statistics for Chemical Engineering at the institute are as follows.

Hope this gives you an idea about the course.

My friend did his B. Arch from BIT Mesra, so I can give you a brief idea about the course.

Architecture depends on your vision, on your projection, and how you see the world. Therefore, college views could differ. Architecture is not like maths which would be the same throughout the world, it is designing and depends on how you can plan your thoughts.

Some of the striking features of BIT-Mesra (Architecture) are as follows.

• BIT-Mesra has a state-of-art course structure. This may not sound important but most of the top universities look at the course structure for Masters.
• BIT-Mesra has great faculty. Most of them get an offer from the most prestigious colleges around the world.
• B.I.T. gives a strong software and structural base to students. They are successful in making you think economically too, very important in a country like India.
• There is a good balance between contemporary architecture and traditional architecture.
• Alumni Network: The Alumni network at BIT-Mesra is strong as well as global. In college, electives like Architectural Journalism, Photography, Conservation, and Urban Planning are good to have and though, they are only a few among so many, it gives you an idea of different fields you can aim for from B.Arch.
• Placements or Job-Scenarios: On-campus training and placements isn't a very happening scene in BIT-M, though there are amazing placement stats among other departments. But things are different for architecture and they have an effective system builtin in the course structure including internships in the final semester. This also happened because students generally have internships finalized (through personal emails) much before the Career Fair starts. 
• Co-curricular: Being a nationally recognized school, great co-curricular activities are happening in the college regularly. These co-curricular lead to the personal growth of an individual and architecture comes out as the winner in many activities and competitions. Great workshops are organized throughout the year at the institute.

Going by the above factors, it is safe to say that BIT Mesra is a good option for pursuing a degree in Architecture.

If by exposure, you mean placements then yes, BIT-Mesra provides exposure to the students. Though you can’t expect the placement to be of the same level as IIMs.

The recent statistics for the Management program at BIT Mesra are as follows.

Talking about the percentage of placements, it's not 100%, but again, if you are skilled enough, you will be placed.

A classic flaw in choosing colleges is that students don't take any of the factors into consideration that includes, including future goals, priorities, and interests.

IIIT Allahabad is specialized to offer only two branches, i.e. Information Technology and Electronic and Communications engineering.

On the other hand BIT, Mesra offers several other courses, only for Undergraduate Programmes.

Now you have to pick what you want and what your goals are before you choose one of them? Is it a career or a college? You should determine which college to attend after contemplating all this.

I know a few people from both the colleges, so I can give you an idea about the institutes. 

Comparison: (Winning Institution - IIIT Allahabad)

• In general, IIIT Allahabad trumps BIT Mesra due to the high facilities and academic standards it provides. The IIIT Allahabad Alumni set high expectations in the industry and if that's what you want, the college has a comprehensive and consistent record of placement. The placement average of the institute is 100%.
• The IT environment at IIIT Allahabad is also great. You will be amazed by the coding culture at the campus. 

Also, make sure that you look at Allahabad and Mesra as towns. In terms of fun and scenic appeal, Allahabad doesn't have anything to provide its students. 

In terms of placements, coding culture, IIIT Allahabad will be better in general.