Comparing the two NITs we know NIT Trichy has a better ranking than NIT Jalandhar. It also holds a stronger brand name. Unless you are extremely interested in Software, I suggest Production Engineering is a better choice. Some points to prove my opinion are:
NIT Trichy ranks in the top 15 engineering institutes in the country from a placement perspective.
More companies visit for campus placements like Amazon, Microsoft, Flipkart, and Cisco.
NIT Trichy has an upper hand in faculty, infrastructure, competitive environment, peers, resources, curriculum, labs, and alumni network.
Many finances, banking, consulting, etc. based roles are offered at NIT Trichy and these opportunities are considerably low at mid-level NITs such as NIT Jalandhar.
Post Graduation, if you wish to switch sectors then the brand name of NIT Trichy will help you along the way.
So don't lose a much stronger brand simply because of a simple stream issue. Years down the line, your credibility will be determined by the brand of NIT Trichy solely and not by production engineering at NIT Trichy.