Which one is better: mechanical engineering at IIT Roorkee or production and industrial engineering at IIT Delhi?

The choice of the Institute as well as the branch is specifically based on your inclinations and only you can make the wisest decision. However, some points that will assist you in making an informed decision are

• IIT Delhi is a winner when it comes to an urban location with a lot of exposure and opportunities outside of campus
• Production and Industrial Engineering is a much lighter program in comparison to Mechanical Engineering and will spare you time and energy for pursuing other hobbies or interests or inculcating new coding skills
• IIT Delhi is the best choice for future entrepreneurs as it helps in incubating ideas and Delhi itself is a hub of startups

However, if you are inclined to Mechanical, then choosing production is not wise. Ultimately, more than the branch and institute, what matters is how well you manage your time and learn additional skills.