Which would be better for an MSc. in physics, IIT Ropar or IIT Mandi?

Rather than answering your question directly, I will answer in such a way that will help you answer it yourself in the best possible way. It’s always best to make your decision in your own. Others can only guide you, the ultimate decision should be made by you. MSc is a degree that opens 3 opportunities, 

• Higher studies like a PhD
• Placement in a private university as a faculty through the IIT campus placement
• Joining a coaching Institute.

Higher Studies: For this, the primary step is to go through the course structures of both the IITs and look at the faculty list and their respective research areas. See if their areas of research align with your interest. Some advanced courses will be introduced which might vary from IIT to IIT. So analyzing the people and course structures is way more important than just choosing the institute.

Placement: Unfortunately, MSc has very limited placement options and chances of landing a good job are bleak even if you are from an active old IIT.

Joining a coaching institute should be your last option.