I think that's misleading. Correct me if I'm wrong, but as I understand it, only the Council can propose legislation, while the Parliament can only accept or reject the Council's proposals [1]. Meaning that the Parliament can neither change nor reverse course - it is completely decided by the Council. All the Parliament can do is limit how fast that course is followed.
Edit: Sorry, what I wrote about the "Council" should have been about the "EU Commission" instead. The Council may in fact have equal power, as you wrote.
[1] Which I think (but was unable to explicitly confirm) extends to removing old legislation. I.e. the Council only has to get its way once, and then we're stuck with a law, unless the Council proposes to remove it. A ratchet.
EU Council (Meeting of EU countries' head of states): Proposes what should be done
Council of the EU (Council of ministers of EU countries): Proposes what should be done
EU Commission: Proposes legislation
EU Parliament: Approves legislation
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".
Note that this means that, crucially, the Parliament also cannot repeal laws. Which means that they can just try and try and try again, and if it passes once, it cannot be withdrawn except by initiative of the commission.
It's like the IRA said to Thatcher, you have to be lucky every time, they only have to be lucky once.
The Commission is the executive branch, so maybe an equivalent would be the Executive Departments?