Having friends in both the institutes, I can say that overall, NIT Durgapur is a better choice among the two. But IIEST is also an excellent institute with national importance. 

There are several factors that affect the placement in both the institutes, according to them here are some - 

• IIEST is a famous and well-established institute in West Bengal, previously known as BESU. But, considering India, NIT Durgapur is more popular. The NIT tag itself is a highlight. 
• NIT Durgapur has several alumni in tech giants across the world. Students from IIEST are currently in IITs and IISc. This is due to their popularity for higher education. 
• Companies recruit fewer students from IIEST, as they have a tendency to leave jobs for better opportunities in higher studies.
• NIT Durgapur also has an excellent coding culture. This increases the chances of securing a job.
• Due to the increase in the number of seats at IIEST, the chances of placement are decreasing.

The following table shows important statistics for both institutes:

NIT Durgapur is a more legit choice for students interested in placement than IIEST Shibpur.