One of my close friends is a third-year undergraduate student in the Department of chemical engineering at IIT Kanpur. After considering all the other choices that his rank allows he finally chose Chemical Engineering.
A majority of IITians take non-core jobs because of their easy availability and much better packages. If you are one of them, then definitely go for Chemical instead of Mechanical. This is because Chemical Engineering has a lesser workload and rigor in comparison to Mechanical, which gives you a lot of time to prepare for non-core jobs. However, it’s important to note that this is applicable only if you are targeting non-core jobs in finance or coding.
But if you are planning to go for Civil Services preferably IES, it’s better to opt for mechanical because you cannot prepare for IES along with chemical engineering.
For core jobs, going for an old IIT like IIT Kanpur is the safest and best you can make Hyderabad doesn't even stand a chance in that case.