By unilaterally assuming universal jurisdiction, the regulation would put European companies in an unsolvable dilemma and would be in conflict with the concept of interoperability that, while recognising different privacy concepts, is necessary in international data flows.
Actually, the EU directive is designed specifically to avoid the inconsistency and ambiguity of different jurisdictions. It will make doing the right thing™ a whole lot easier. Turnkey systems will be come available and legal processes will be standardised.
Data can be processed abroad but companies will have to contract to the EU data protection standards. This might stop personal data leaking out of outsourcing companies as is currently only too often the case.