IIEST Shibpur is better than BIT Sindri in terms of placements, infrastructure, and academics. There are a lot of resources available to you and if you are willing then it will be a great learning experience for you.
The college is more than 160 years old and thus has a huge list of alumni base. It has recently been converted to an Institute of National Importance (INI) and is equivalent to an NIT.
The campus also offers a great scenic view. Some of the placement stats of mining engineering for the year 2020 are given below.
So IIEST Shibpur edges ahead BIT Sindri according to the opportunities they offer. You can definitely talk to other students and form your own opinion as well.