Maharashtra

St. Xavier's has a better brand name than Sinhgad Institutes. Some of the important points while selecting an institute - Accreditation of the institute, institute's infrastructure, teaching faculty, specialization offered, past placements records, tuition fees, city preference and industry interface as both the institutes are having the campus in Kolkata and Pune. Industry exposure is good for students in either of the college. If possible a visit to college is better option to get a reality check. Also, get in touch with college alumni's through the social network to get information about the latest changes if any.
You can compare the course fee, placements, students review, facilities offered, seats offered on the below link-
https://www.shiksha.com/resources/college-comparison-122492-83763

IBS, Mumbai is better than IBS, Gurgaon. IBS, Mumbai is a decent college. One of the best out of all the other with good placements in mainline streams such as finance and marketing. Placements lag in streams like HR, operations and IT.Honestly, it has got the excellent faculties and you'll have a lot to learn.
Great course curriculum. It lacks in terms of large campus but has got ample co-curricular activities and events throughout the year. It has got a good return on investments with the average package lying around Rs 6 lakhs.
Irrespective of the placements and other things, studying at IBS is worth an experience and it will teach you. IBS, Mumbai is a decent college.