Which is better: IIIT Allahabad or BIT Mesra?

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.