Hii there,
There is nothing such criteria for differentiation in between these three types of college. If you have any choices then instead of seeing whether it is private or government kindly see a criteria like fees, study, placement, facilities also your budget matters. Some good colleges are

• IHM Pusa ,new Delhi

• Institute of hotel management, catering technology and applied Nutrition, Mumbai

• IHM Bangalore

• Christ University, Bangalore

• IHM Hyderabad

• IHM Chennai

Hope it helps. Good luck!!