IIIT Srirangam should be preferred to IIIT Sri City. Though both were established in 2013, IIIT Trichy, or IIIT Srirangam as it is popularly known due to the name of its location in Trichy, has been functioning its temporary campus at NIT Trichy, which happens to be its mentor institute as well, campus until 2020.

Another factor which tips the favor towards IIIT Srirangam are its placement records. The institute also records a highest internship package of INR 2.25 lakhs. 

IIIT Sri City, though has been mentored by IIIT Hyderabad, has been functioning temporarily at the Institute for Financial Management and Research, Sri City campus. The mentor institute carries little importance, but the location of the temporary campus really does. Thus looking at these parameters, IIIT Srirangam is preferable.