Des aspirant,

If you were to take my opinion then i would surely choose bit mesra because iiest shibpur is known for its ug b.tech or m.tech course . It's not known for finance.

Whereas Bit mesra bba/mba course is also renowned and is considered to be good in terms of placements ,value for money, academics and a few more.

So, my final advice for you is to choose bit mesra over iiest shibpur.