English skills aren't the best but I don't think that's the issue. Substandard education drives the unemployability and poor infrastructure drives the lack of jobs outside the bigger tech metros (Bangalore, Hyderabad, Mumbai IMO).
Its a vicious cycle where uneducated citizens select equally uneducated lawmakers (because susceptible to propaganda/lies easily). The uneducated lawmakers don't have much incentive to improve education, because that will affect their election results, next time around.
And turning to private institutions is of no use. They have neither the good will nor the cash flow to actually do something about this problem...
Is one better than the other?
I went through a mediocre private college - I can safely say that besides two or three of my profs, most were absolutely useless and couldn't code their way out of a paper bag. The syllabus is also pretty crap - when it wasn't random electronics courses to pad the syllabus, it was the same course slightly tweaked and presented by a different prof. There was no mandatory course where a large-scale programming project was to be made. Version control, shell usage, practical database usage, and many other basic things were not taught at all.