Have I done a mistake in choosing IIT Delhi mechanical over DTU CS? I preferred to do CS, but due to ego, I chose IIT Delhi.

I don’t think anyone choosing IIT Delhi over any other engineering college has made a wrong decision given the opportunities and life experiences that come with it. While both are crucial, your choice of Institute is more important than your branch. 

Here is a friend's journey for your reference l was a BTech student (Civil) at IIT BHU with a rank of 3600. 

• First, he completed a Nanodegree program from Udacity in Self Driving Cars and Machine learning
• Next, he worked as a Derivative Trader in Future First where he performed Machine Learning and Deep Learning algorithms.
• After gaining great experience and exposure he joined Quantela Inc for 2 Years where he worked as a Data Scientist.
• Today, after a lot of job switches and immense experience he is working at Derq in Dubai as a Machine Learning Scientist and doing Online MS from Georgia Tech University in Computer Science.

This journey of a 7-pointer Civil Branch student to a high-tech CS company proves that branch does not matter in the end. He made the most of his campus life and kept struggling to switch his branch and eventually succeeded. That being said, you have made the right decision as only IIT Delhi can give you the right set of opportunities and exposure and not DTU.