The 'institutions' consist of the Parliament (directly elected, but with limited powers), the Commission (effectively the Civil Service, develops policy but has no power other than what is delegated to it), and the Council (where each country is equally represented, and is the real decision making body of the EU).

So in fact the institutions are entirely democratic, and arguable more democratic (and less dysfunctional!) than their counterparts in the US and China (the other two super blocks).