As a student you should check the following areas and take them into consideration while choosing a particular institution.
Research- VNIT, and COEP beats VJTI in these criteria. Students can do research here under college professors on winter vacations.
No of recruiters
Highest Recruiting Branch
Student Activities- VNIT excels in expectations than COEP & VJTI with myriad festivals, clubs, and extra-curricular.
Research after Bachelors’- Lots of VNIT students get themselves into research work after their graduation. However, there is no available information for VJTI and COEP.
Considering all the aspects listed above, VNIT seems a better choice for mechanical engineering than COEP Pune and VJTI Mumbai.