Daksh if you are getting a very good top NIT with a good branch then you can think of switching a lower rank IIT with it but keep going to IIT Hyderabad instead of IIT out of your bucket until and unless you are only able to end up in some of the ultra new IIT like IIT Jodhpur, IIT Goa, IIT Jammu, IIT Dharwad etc. These are the ultra new IITs which have been recently started and will take a few years to settle down in this market. By studying in any of these IITs you will get an IIT tag but in the terms of placement and studies, it will not be on par with other IITs. 

Other than these ultra new IITs if you end up in any of the decent branches in any of the other IIT then don't think of skipping it and joining IIIT Hyderabad because the tag which you will bear and the alumni network which you will have will help you all throughout your life.

Feel free to ask if you have any more queries. All the best!!