Hey Janvi

It depends upon which level of Public (Government) Institute it is. For example if  we take example of Indian Institute of Technology (IIT) and National Institute of Technology (NIT) or state Universities like Delhi Technological University (DTU) or Jadavpur university, considering them these are one of the best and reputed colleges in the country with an impeccable academic and student' success record.

Whereas there are private university like BITS, Pilani, Manipal Institute of Technology, and Amrita School of Engineering, which has also have similar academics but a bit change in curriculum and other facilities.

Mostly it depends upon the students, the locality he/she is comfortable in and the fees of colleges, Private colleges have higher fees structure than government colleges.

If you get admission in any good, reputed government college then you must prefer it, as it has more value than the private.

For further doubts, ask us. All the best