ECE and CSE are somewhat similar considering they have similar foundational courses. As a result, CSE and ECE students can pick skills from the sister course.
Quite often, ECE students become great coders and get placed in IT companies while some CSE students seriously get into signals, circuitry, and robotics.
As for NSIT and IIIT Delhi cultural differences, ECE in NSIT and DTU are better known and regarded than ECE in IIIT Delhi interns of placements and course structure. IIIT Delhi is more famous for its CSE branch. So, choose IIIT Delhi only if you are willing to do a masters in CSE.