[alephnerd]

It depends. Some private schools like Delhi Public School Barakhamba are extremely prestigious, but making a private school is very easy so quality control is trash.

Sometimes private schools can be shittier than the government run schools (eg. in the town my family is from in Himachal) but in other places the private schools will at least not have absentee teachers (a common issue in much poorer regions of India).

P.S. the public school moniker for some Indian private schools is a holdover from the British era. Most modern private schools don't call themselves "public" anymore - they prefer being called "International Schools".