IT in NITK is the most sought-after branch after CS and EC. You should also be aware of the status of NITS and BITS. NITs are usually national-level institutes, but the onus of choosing your preferred branch and institute finally depends on you.
NITs have always been better than private institutes. Look at your area of interest. Do you like to tinker with electronic objects or is coding your forte? Once you clear this out, you will have a clear idea about what to choose.
But, if you are unable to make a decision, look at placements if you are going to look for a job in the future. Students from CS and IT get paid really well with higher chances of bagging a job as compared to other branches.
As far as these two colleges are concerned, NITK has better placements for IT. BITS Goa is good too. Overall, you will not regret choosing either of these two colleges but in the end, it all boils down to your interests.