Firstly, I don’t think that the average package of IIT Mandi is more than IIT Guwahati. I think you are confused and looking at the placement statistics of different departments, disciplines, and programs. IIT Guwahati usually releases combined placement statistics for B.Tech, M.Tech, Ph.D., and other programs.

Even if this wasn’t the case, one should look at the placement percentage which denotes the ratio of people that applied for placements and those who got placed. Considering this, there are 2 instances under which IIT Mandi’s average can be higher than IIT Guwahati's.

• Out of the total batch, a maximum did not get a job while those who got, one received high packages, thereby increasing the average. 
• A few extraordinary placements might have affected the overall placements bringing up the average.
• There are more SDE jobs and very less core engineering, research, consulting, and management jobs. SDE jobs are the highest paid so the average at such institutes will be higher.

Thus, I don’t find it logical to compare the mean only. Mode and Median should also be given due importance. The placement statistics are said to be appropriate only if Mean Mode and Median are almost similar. Having a high Mean literally means that a handful of students got high packages while the majority of the batch received below-average packages. 

All I mean is that comparing two institutes on the basis of their average packages is not justified. I don’t necessarily mean IIT Guwahati is better than IIT Mandi.

When considering Engineering Physics, the choice of the institute is a secondary factor while your inclination towards Physics is the primary concern. The course is not for those who take it casually without genuine interest in it.

I think IIT Guwahati is a better institute for EP. Those who have a branch change of mind should take the batch strength into consideration as only 10% of the batch is allowed to opt out of EP.

Thus, unless you're certain of EP, I would recommend you go for BITS or top NITs. This will help you if you are looking for a core course.

Rather than giving you a direct answer, I am going to evaluate all The aforementioned institutes individually on the basis of some common parameters like placements, brand name, campus life, opportunities, and alumni.

IIT BHU ECE

• Core placements are rare and students mostly build their profile for software development companies by becoming proficient in various programming languages, doing competitive coding, doing projects, and trying to build a computer science-inclined profile. A handful of students target core engineering roles.
• The brand value is similar to other colleges mentioned
• The campus is rather old and might disappoint freshers expecting a good college life.

IIT Guwahati ECE

• Unfortunately, I have no knowledge about this Institute. However, I recommend you contact the seniors of IIT Guwahati for the same.

IIT Hyderabad Maths and Computing

• Usually, MNCs attract top-tier software and financial services firms. If you are a hardworking student, it wouldn’t be difficult to secure amazing offers at top firms.

IIIT Hyderabad CSE

• IIIT H has possibly one of the best computer science departments in the country. 
• You have to do core computer science courses right from the first year.
• Many students get selected for Google Summer of Code and IIIT Hyderabad has its alumni in top-notch firms. 
• Being highly academically oriented, IIIT Hyderabad has minimal campus life and extracurricular activities.

Ultimately, it’s a matter of preferences and what you are looking for in your degree.

Both BITS Goa Pilani and IIT Guwahati/Kharagpur are well-respected institutions with dynamic mechanical engineering programs. The choice between them depends on a variety of factors like location, campus culture, available resources, and specific research interests. BITS Goa/Pilani is known for its strong focus on research and innovation, while IIT Guwahati/Kharagpur is known for its strong faculty and resources.

My brother was a student of Mechanical Engineering at IIT Guwahati and I have a few points as to why IIT Guwahati is better than BITS

• IIT Guwahati has a spectacular campus surrounded by natural beauty giving it a resort-like ambiance.
• The accommodation facilities are top both with every student getting single rooms right from the first year
• Your passions and hobbies are given importance and you will find many that share your interests
• Excellent sports facilities
• The Mechanical Engineering department of IIT Guwahati has excellent faculty, especially in fluids, solids and thermal.

A few drawbacks of the institute are

• Its remote location leaves you isolated with no place to hangout near
• The Mechanical branch has mainly boys only 

All in all, IIT Guwahati should not be your choice if you want a laid-back college life filled with fun. However, if you are sincere about your career and want to pursue mechanical engineering, IIT Guwahati is the right place for you.