We explore one dimension of global value chains: the complexity of organization of international production within multinational business groups as represented by the worldwide control chains. Exploiting a unique dataset that matches affiliates with parent companies, we first propose a measure of entropy for the control chain borrowed by hierarchical graph theory, then linking it to the performance of affiliates measured by productivity. We restrict our focus on a sample of some 22,211 firms located in the New Member States of European Union and controlled by ultimate parent companies located in EU-15, confronting them with individually owned foreign businesses. We find that simple affiliation to a multinational business group implies a different firm performance, although the effect becomes non monotonous for relatively higher levels of complexity. Among the benefits of affiliation we find in particular that financial constraints are softer whatever the size of the multinational group.