Can I choose production eng in NIT ,TRICHY or Mechanical.eng in IIITDM, KANCHEEPURAM?
depends solely on your interest! Moreover, it aslo depends on what you'd want to do after your engineering.
What I can say is Mechanical Engineering is a core branch so it fetches better packages while placements and moreover, it has a broad spectrum of opportunities as compared to Production.
But, after having done production engineering if you go on to do MBA in operations, that would open great windows of opportunities so, suc smart combinations may help you reach the top of the ladder of success.