Which one would be better: production in Jadavpur university, power in Jadavpur university, mechanical in Jalpaiguri, or government engineering or mechanical in Kalyani govt. engineering?

Choose the course that interests you, college is a secondary thing. Here are some of the facts that may help you in choosing the right branch for you.

• If you want to work in PSUs or Govt. sectors, it’s better to not choose Production Engineering as there are fewer recruiters.
• Jadavpur is the best college you can get through WBJEE. If you choose Production or Power in JU, you will have good on-campus job opportunities.
• Production Engineering is a branch of Mechanical Engineering itself. The syllabus will be more or less the same. 
• Mechanical at Kalyani University will be slightly better than Jalpaiguri. You may not get lucrative job packages at on-campus placement from Kalyani University but in the long run, you will have a much better hold with your Mechanical degree. You can expect well-paid jobs in the future. 

Your future will depend on the branch you are choosing so choose according to your interest. All these Universities will offer you enough opportunities and resources to prosper. It’s up to you to use that well.