Amrita and VIT are very different from each other.

Amrita University has a controlled environment, high focus on academics, and good placements. For a bright career, Amrita is a great place. But its campus life is very dull. One has to find a source of entertainment and growth on our own.

VIT offers a vibrant and lively campus. But one has to mostly rely on self study. 

Both the colleges are good for a B.Tech. Make a choice based on your own caliber and priorities. 

I will refrain from giving you a detailed answer because others have already done so. Rather my explanation will be simple yet impactful 

• IIT Patna is a new IIT so you can avail the benefits of the IIT tag only and the institute in itself is just average. 
• MNNIT Allahabad on the other hand has a rich legacy as it’s an old college. It has extensive alumni and is one of the top NITs.
• ISM, now an IIT, has the combined features of both aforementioned institutes. It’s old and also has an IIT tag attached to it. 

That being said, my preference order among these institutes is, ISM>IIT Patna>MNNIT