Which is better out of DTU, NSIT, VIT Vellore, BITS (any campus), NIT (top 3) and IIIT (Hyderabad and Delhi), placement-wise and education-wise?

On the basis of placements, I would rank the aforementioned institutes in the following order

Bits Pilani, Pilani Campus>|IT H>Bits Goa>Bits Hyderabad>Top 3 Nits>|IT Delhi/NSUT>DTU

BITS Pilani has a better placement scenario than IIIT Hyderabad although its average package is less than IIIT Hyderabad, this is because BITS has a number of branches and the average package is calculated after considering the packages of all branches whereas IIIT Hyderabad has only two branches ie CS and ECE. Both these branches are top branches so automatically its average package becomes higher than BITS Pilani. If you compare the placements of the CS branch alone, BITS Pilani will have the upper hand. However, if you want to pursue a career in research in CS, ten choosing IIIT Hyderabad will offer better opportunities. Basically, IIIT Hyderabad will make you a better coder whereas BITS Pilani will make you a better engineer.

It's important to note that the above ranking is based on placements alone and if you consider the research culture, then NITs will fare better than BITS mainly because they are government institutes and receive huge funds solely for the purpose of research.