There is no clear winner between IISER Pune and IISER Kolkata. IISER Pune and Kolkata are quite old and equally reputed. IISER Kolkata is more known for its Physics degree. While IISER Pune is reputed for Biology. 

Comparably IISER Pune has a better location. So, students receive better employment opportunities. 

IISER Pune is better than IISER Kolkata in terms of the opportunities that you will get. IISER Pune has more tie-ups than any other IISER. It is a member of the CMS-CERN group and Royal Chemistry Society, London. There are many research institutes in the vicinity of IISER Pune. NCL, IITM, NCRA, are a few such institutes. As it is situated near Mumbai, professors from TIFR, often take full semesters at the institutes. The campus has great facilities with high-tech research labs and other necessary facilities. For Physics, in terms of faculty and curriculum, IISER Kolkata is better than IISER Pune. However, for Chemistry, Biology, and Mathematics, IISER Pune is definitely better.