First, let me say that I think I'd rate EU as being more complex than Advanced Third Reich but less so than Advanced Squad Leader or Star Fleet Battles. EU covers world history from 1492 to 1792 from a Eurocentric perspective. It's playable in two modes. These use only the rules for moving and fighting with military units, and enough of the economic rules to allow you to raise and maintain armies.
Units are variously-rated leaders, armies, fleets, and land and naval detachments.
Battle scenarios require between 2 and 5 players, each representing a state or coalition involved in the war. The campaigns pretty much require 6 players, each playing one of the major states of the period. And it's a beautiful mess. Erich may have been charitable in blaming the rules problems on the translation from French into unidiomatic English. From what I've heard from Francophones, the French rules aren't much clearer.