It all depends on how is the financial condition of your family. Engineering fees are not as high like MBA, so if your parents can afford it and if the private college is better than the government college, then you definitely should go to the private college. Private college often gives better exposure to students as compared to a government college. But if the government college is better, then you should clearly choose the government college. Choose the branch which you love, do some research on what is taught in which branch and see which suits you better.

Thanks.