What should I choose: EC in a government college or computer engineering in a private college?

Both CSE and ECE are equally good branches. You are advised to chose branch based on your interests, brand image of college and it's facilities, faculties, placement records.

According to me you should go for ECE in Govt. Engineering colleges because now a days placement scenario for ECE is increasing day by day than Computer Engineering.And if you did from a Govt. college then you dont have to worry. So all the very best for future !!