What should I choose: NITK CSE or IIIT Hyderabad CSE?

The decision of choosing one between NITK CSE and IIIT Hyderabad CSE depends on what kind of college life you are looking for. To be frank, if you want a dynamic campus life with an equally good but light curriculum, NIT Surathkal is better than IIIT Hyderabad because the matter has a very rigid campus life that focuses entirely on academics. NIT Surathkal will give you a huge baggage of memories, a good job, and some good connections. But IIIT Hyderabad will help you become a person of responsibility whose only focus is building a career. 

NIT Surathkal brings you together with people from all corners of the country which makes the experience better. IIIT Hyderabad on the other hand has only two branches - CSE and ECE. So the former may not make you a very talented CS engineer but will surely develop your personality as a whole.

So the best way to decide is to analyze your inclination, and then make an informed decision.