Currently, is IIEST Shibpur, formerly BESU, better than Jadhavpur University?

IIEST Shibpur offers integrated MTech for engineering streams. So, first, be clear if you want to pursue MTech from an institute that does not have a record of producing post-grads like IITs or other universities abroad. 

Comparison:

In academics, there is not much difference between JU CS and BESU CS.

In fact in the present scenario, JU CS has better placement statisticsas compared to BESU CS.For this reason, sometimes BESU CS/IT graduates join IITs after the completion of their course and often end up in the same firms their fellow JU mates are working in for 2 years. 

BESU got updated to the status of IIEST quite recently. It will take some time for the institute to improve its infrastructure and academics. Being an institute of national importance, the institute is attracting good facilities and campus recruits. 

The bottom line is if you are sure that you want to pursue integrated MTech, IIEST CS is not a bad option. Be it JU or BESU, the institute does not matter that much. If you are hard-working, you will excel.