If IIT is the most important thing in your life then you should definitely choose the new IITs. You can take any trade at the old IITs because that makes much more sense considering there are already so many new IITs. The government isn’t going to stop opening new IITs, so the question arises that IIT is a brand name and that by the virtue of being an IIT, it should be preferred over all other non-IIT institutions.
When IIIT Allahabad was opened by the Central Government, it was given the status of an IIT. With the coming of the IIIT Act 2014, it is a de facto IIT for IT. IIIT Kancheepuram was mentored by IIT Madras whereas IIIT Jabalpur was mentored by IIT Kanpur. These centrally funded IITs can also claim the privilege that the new IITs claim which is, that they are an IIT and that they have been mentored by old IITs so that they should be preferred. People see that extra ‘I’ and do not apply the same logic and create a hierarchy of their own making and choosing that IIT> IIIT which is not backed by any evidence.
In the 2015 Allahabad High Court case, the court struck down the cancellation of the appointment of faculty using UGC norms as the excuse. The court said that since it was set up as an IIT, it must comply with IIT norms.
You should make a decision based on the learning atmosphere and the reputation of the college in the area which you want to pursue. In QS World University Rankings for Computer Science and Information Systems, IIIT Allahabad was ranked 11th in India just after the old IITs. The parameters for ranking use the quality of research and industry reputation. Moreover, the IITs are for science and technology having on an average 20 departments whereas IIIT specializes in IT.