The EC is only the inter-government stuff. To be fair, you'd have to include all the employees of all the member states' governments too; or alternatively, compare e.g. London governmental employees, though scaled to population and leaving out actual England and UK administration.

For example, http://www.tfl.gov.uk/corporate/about-tfl/investorrelations/... shows that Transport for London (buses, trains and underground) alone employs about 18,000 people (and probably quite a bit higher now).