Which is better for competitive programming: Jadavpur University or IIEST, Shibpur?

Any college can be good for competitive programming. It all relies on you to educate yourself, to learn new strategies, and to spend hours coding. 

• Anudeep Nekkanti is one such example. He was recruited by Google and qualified for ACM ICPC world finals. If you look at the name of his college, it's not one of those elite ones. 
• There was no competitive programming pattern in BESU/IIEST until recently. But many students have taken competitive programming platforms such as Codechef and HackerRank over the last few years.
• You can search the Codechef Rating System site to verify it for yourself. You get a college-wise database of the number of students actively engaged in competitive coding and their results using this platform.

Lastly, don't support the myth that the only way to prove yourself as a coder is competitive programming. There are other coding fields as well. In this sense, do not consider that there was no "real coder" in IIEST because there was no competitive coding pattern previously in IIEST (BESU back then). 

Some of the alumni of the institute are working in top companies in India and overseas and have never been interested in competitive coding.