In my opinion, the institute is more crucial than the branch as academics rarely matter for an IITian. What actually matters is how the college molded him from a fresher to a mentally stable and talented person who has honed his talents to the fullest through maximum exploration.
That being said, I would recommend you to go for IIT Bombay irrespective of the branch you are able to make it into.
Overall, IIT Bombay will give you a sense of freedom to explore everything and broaden your opportunities.