Should I change to a Delhi School for DTU or NSIT?

Yes, you should certainly consider changing to a Delhi School for DTU or NSIT. Like every state Delhi too has institutions where there is a reservation for Delhites. DTU and NSIT are among the top engineering colleges and the fact that both of them are situated in Delhi gives immense opportunities to the residents. 

Both DTU and NEIT are under the purview of the Government of National Capital Territory(NCT) of Delhi so they have an 85% reservation for students who do their schooling from Delhi.

So if you are a Delhite you have to compete with 85% of the batch which is easier than competing against 15% seats for remaining states. Here, you can get CS even with an average rank if you are a Delhite but it may be impossible if you are from another state. So yes, shift to Delhi and avail a plethora of opportunities!