CSE has a strong future and my friends from Patna CSE have landed jobs at Amazon, Moonfrog Labs, Flipkart, Directi etc. and these are amazing companies to work for and pay extremely well. Additionally technologies such as AI/ML/DL/Neural Networks/VR/AR etc have a big market and CSE courses essentially build your framework for learning these.
So in my opinion its a clear choice – CSE at Patna. However if machines fascinate you, you can think of Mechanical at Roorkee but CSE is better anyday and has interesting and challenging problems to be solved. Enjoy!!