Mechanical Engineering

Well both are good. Better if you choose CVRCE. For further assistance, you can comment below.

Mechanical engineering is a major engineering and development sector, highly growing with good plateforms,
Manav Rachna University is best university in Delhi NCR with best infrastructure and faculty. The plus point of Manav Rachna University is that it offers the best placement with maximum up to 18 LPA.
http://manavrachna.edu.in/university/

Dear, production engineering is a part of mechanical engineering. If you want to go in manufacturing industries & want to be a specialist in production then you can do the your B.Tech course in production engineering. In mechanical, you can learn about all the energy subjects like thermodynamics, refrigeration and air conditioning, fluid mechanics internal combustion engine and some part of production engineering.