Which one should I choose, Aerospace at IIEST or ECE at Heritage Institute of Technology, given that I'm interested in both?

Seeing your interest in both branches, IIEST has a wide scope of diverse cultures and you will find many students from all over the nation. 

IIEST Shibpur offers great exposure in terms of academics as well as extra-curricular activities along with the interactive clubs and fun happening fests. It comes under the Government of India and is one of the NIT. 

However, Aerospace Engineering is not a trending branch anymore and it was in the limelight a decade ago. To open up more opportunities, you will be required to pursue a Master’s or prepare for the competitive exams to get a decent job. 

ECE at Heritage Institute is more prominent but being a private college, it is not up to the mark as compared to Aerospace Engineering. The placement opportunities at HIT are not good. Therefore, all you can do is to opt for IIEST, get a decent aggregate, and change the branch from Aerospace to ECE in the second year.