The European Commission has strong powers because it has the monopoly of proposing (initiating) laws in the EU. However, the Commission is not a directly elected body.
The Lisbon Treaty provides for a super qualified majority in the European Council - 19 of 28 prime ministers and presidents also representing 260 of 352 weighted votes - to elect the Commission which must then be approved by an absolute majority in the European Parliament.
Federalists have proposed that the Commission President and his colleagues should be elected by the European Parliament and be responsible to the Parliament.
Euro-realists and eurosceptics propose that every national parliament elect its own national Commissioner, who could also be sacked by the respective national Parliament.
After the European elections in 2014 the European Parliament established a new practise where the Commission President is elected by the Parliament.
See Democracy