I think I am qualified to answer this question as I graduated from IIT Madras Aeronautics department and I am working for Boeing in the USA.
You should choose IIT Madras due to following reasons:-
For more detail Refer - https://www.iitbbs.ac.in/index.php/home/placement-2023
https://internship.iitm.ac.in/downloads/P&I_Report_22-23.pdf
IIT Madras has a great Mechanical Engineering branch. The departmental lab and workshop are well-equipped with cutting-edge instruments. IIT Madras Mechanical dept. has a well-experienced faculty pool. Many faculty members are actively pursuing research projects.
IIT Madras placements are good for Mechanical Engineering. Around 85% of students get placed from the branch. The average CTC received by the students of the branch is around INR 12 LPA.
Aeronautical Engineering is still one of the evolving and emerging domains in India. Dual Degree is a more research-oriented degree. According to the statistics, among the students pursuing dual degree programs in Aeronautics from IIT Madras, 79% are placed with good packages in the academic year 2018-19. As per the record, a total of 20 students registered 14 got placed with a good package. The packages offered here range from 4.8 LPA to 20 LPA. Still, finding a good placement package is a matter of struggle with this course.
BTech in Electrical Engineering offers a good course curriculum and is highly oriented towards the industry based platform. It provides a good opportunity in the aspect of placements. According to the statistics of the year 2019, IIT Bhubaneshwar had 86% of placement in Electrical Engineering with an average salary of 11.4 LPA which is highest among all the other IITs. Some of the students are placed in ISRO too. So, opting for the B.Tech program in IIT Bhubaneshwar is a good choice if you are looking for both research and good job opportunities.