Which is better for a person getting JEE rank greater than 3500: Get brand name of IIT without top-notch branch or join NITs/DCE/NSIT with CS/EE?

If your rank is more than 1000, you’ll probably not get CS/ EE in any good IIT. But if you still wish for an IIT tag, I would recommend you go for a more relaxed branch. This means, picking the branch with the lowest closing rank. I am saying this because apart from the CS/EE/Mathematics group, all the branches come under the category of “others”. Unfortunately, all these “other” branches are equally placed.

• The coursework, curriculum, and labs are very bland, boring, and outdated. With these branches, a good CGPA and extracurriculars will be the saving grace for your resume. 
• A lower branch will allow you to secure good grades more easily and you will get time to pursue extracurriculars. 
• By doing courses on Coursera and Udacity and making open-source contributions, you can become skilled and learn in coding/programming. Through various online platforms, you can get in touch with software companies in the valley. 

If you are passionate about a field, be it Mechanical or Chemical, definitely go for it. With a passion for your field, you will secure a good core job or can even plan your Phd. in that domain. I would also recommend you check the integrated MSc. courses in Mathematics/Statistics/Physics. They might be a better and more beneficial choice.

As far as NSIT/DCE/NITs are concerned, I would recommend you talk to some seniors from the CSE/EE branch to get a better idea. Otherwise, go for a lower branch in the IITs if you do not get a “top notch” branch at them.