Firstly, you should know that there is no difference in the facilities and reputation of the colleges, Although BITS ranks better as an engineering school. BITS Pilani ranks #30 on NIRF's Engineering rank list and IIIT Allahabad ranks #103 on the same. But you should focus on your monetary capacity in consonance with your future plans before applying. 

My cousin studied at IIIT A and the following points are based on his experience:

• IIIT A is an excellent place to study coding. The classes are good although the syllabus has to be maneuvered because it's tough. You can manage it through attention in the classroom.
• Attendance is an important part of the academic process here because IIIT A has a 75% mandatory attendance rule.
• Without a doubt, BITS has a higher fee range as compared to IIIT A, about 7 LPA for a 4-year program.

Here's a table comparing both institutes:

Lastly, if you love the mechanical stream and are truly motivated to study Maths and Physics then you must go for it. Mechanical is a vast field as well because you'd learn everything related to mechanical processes and even production scheduling. So clearly check your interests and goals before deciding.

The best would be to go for a B.Tech from BITS Pilani and then an MBA degree from IIM/XLRI etc.

IPM at IIM Indore gives you an IGNOU graduate degree and then a diploma. Even though you will do the last two years together with the PGDM students selected via CAT, you won’t get the same status as them. It will take a couple of years to get acceptance. Additionally, the legality of the course is vaguely defined. 

Choosing one of these options also depends on your career orientation. If you want a job in the technical field then doing a B.Tech from BITS Pilani is better. Go for IPM from IIM Indore, only if you are certain you want to get into management job roles.

The MSc. Honours at BITS Pilani is a highly recommended course for every student who is interested in a combination of Science and Engineering. It is an excellent course provided by the institute, with great opportunities for students in various fields. The points below give a brief overview of the course of MSc. Honors provided by BITs Pilani.

• The course provided by BITS Pilani is a dual degree course, which comprises five years of study in total.
• After the first year of the course, you will be provided with subjects that belong to different branches of engineering (B.E). This is a great opportunity to explore such subjects from different streams, along with the conventional science subjects. You will get several choices in the selection of subjects and choose between topics according to your own decision.
• BITS Pilani is predominantly an engineering institute. Therefore, there are numerous minds in the institute for several technical works and inventions. The institute has earned recognition in the fields of space-travel bots, humanoid robots, Formula-one style cars, and a lot more.
• Students from BITS Pilani have been selected in Google Summer of Code several times, which is one of the most prestigious competitions in the world in the field of computer science.
• Other than the field of academics, students of BITS Pilani get the freedom to perform anything of their choice and achieve a good position in it. There are several musicians, dancers, painters, poets, debaters, etc among the batches of BITS Pilani, and even students with multiple talents in it.

Therefore, BITS Pilani provides an appropriate ground to cherish any kind of talent of students, which is a great aspect of the institute.

First of all, you need to understand what you want. Do you want higher education or a placement? Then ask yourself whether you want only computer science because you love the subject or simply because you want a good placement.

• If you love computer science, then do not worry and join NIT Calicut. You will learn it in an elaborate way and can then pursue a master’s or doctorate degree. 
• The fee at NIT Calicut is also lower than that of BITS Pilani.
• However, if you are like the majority of people who want CSE for placements, then I would suggest you consider BITS Pilani or any of its other campuses. 
• You have to understand that a CSE degree is not compulsory to learn to code. 
• If you join ECE or ENI programs and learn to code yourself. You can easily land a job in any IT company. 
• The salary package you will receive at BITS Pilani (any campus) will be better than that of NIT Calicut.
• The college life of BITS Pilani will also be very good. 
• You will not have the pressure of attendance. 
• There are lots of extra-curricular activities you can participate in also.

ENI and ECE are technically different branches but they are almost the same. Except for the high fee of BITS Pilani, I do not feel BITS Pilani or Goa campus is anything less worthwhile than NIT Calicut. In fact, if you want only placements, then BITS Pilani any campus should be your choice.

Among the given options, BITS Pilani CSE is relatively better. Here is why.

• BITS Pilani has a strict no reservation policy so you will have a better peer group there.
• The institute follows a relative grading system. Your grades will depend on your batchmates and the one who has scored the highest grades. It can be a bit hard there to get good pointers because of the tough competition.
• According to the recent placement highlights, the highest package offered by BITS Pilani was INR 45 LPA and the average package was INR 18.05 LPA. The percentage of placement this year has been 99%. Top recruiters are HSBC, Linked In, Adobe, etc. While the highest package recorded by IIIT Allahabad was INR 43 LPA with the average package being INR 20.83 LPA.

As for the difficulty level of the curriculum, it’s entirely subjective.