> The Parliament acts as a co-legislator with equal legislative power in this process

The EU Parliament doesn't have equal legislative power. EU Commission proposes legislation, and the parliament can only accept or reject. Of course informally they can discuss with the Commission and let the Commission know what they would or would not pass.

> effectively representing the citizens while the Council represents the member states governments

This is true. But you maybe forgot another body, the EU Commission.

EU Council, Council of the EU: Represent member states

EU Commission: Represents the EU

EU Parliament: Represents the citizens

I guess US doesn't have a body like the EU Commission, that is not elected and that represents the interests of the "deep state".