The European Commission is one of the most undemocratic institutions. These people [the EU commissioners] were not elected by anyone and they are not accountable to EU citizens.
The European Parliament is powerless, so few people want to take part in the election. Is it even important who you vote for? Even a landslide win in the Parliament will have no effect on the Commission or the Council. And that is exactly where the real power lies. The European Parliament has no real influence on the actual important policy areas.
After the EU Parliamentary elections, one of the first tasks of an incoming Parliament is to elect a new President of the European Commission. Member states (the Council) nominate a candidate for the post, but in doing so they must take account of the European election results. Moreover, Parliament needs to approve the new Commission President by an absolute majority (half of the existing MEPs plus one). The EP members can reject a candidate and had exercised this power in the past. The President and the other members of the Commission are subject to a vote of consent, as a body, by the Parliament and are then appointed by the European Council, acting by a qualified majority.
As for the powers of the European Parliament, it is one of the two co-legislators - which means that without it, legislation is not adopted. It also approves the EU budget, has control powers and the right to intervene before the European Court of Justice.
See here for other disinformation cases about the European Parliament.