Big platforms dominate the new economy landscape. Colloquially known as GAFA [Google, Amazon, Facebook, and Apple] or FAANG [Facebook, Amazon, Apple, Netflix, and Google], the high tech big data companies are charged with using the power of their platforms to squelch start-ups, appropriate rivals’ ideas, and take and commercialize the personal data of their users. Are the platforms violating the antitrust laws? Should they be broken up? Or are they the agents of progress in the new economy? On these points, the United States antitrust law and the European Union competition law may diverge. The Competition Directorate-General of the European Commission has brought proceedings against or is investigating Google, Amazon, Apple, and Facebook. Germany, under its own competition law, has condemned Facebook’s conduct. Meanwhile, in the United States, authorities are skeptical, but they have commenced investigations. This Article is a comparative analysis of U.S. and EU law regarding monopolization/abuse of dominance as background to understanding why EU law is aggressive and U.S. law may be meek in the treatment of the big tech platforms. First, it examines the factors that underlie the two perspectives. Second, it considers three cases or problems—Google/Comparative Shopping (EU), Facebook-Personal Data (Germany), and dominant platforms’ acquisitions of start-ups that are inchoate competitive threats, such as Facebook’s acquisitions of WhatsApp and Instagram. The Article considers what lessons the latest Supreme Court antitrust decision, Ohio v. American Express (AmEx), holds for the analysis of the big data antitrust issues. Third, it asks what U.S. antitrust law and enforcement should do. It concludes that U.S. antitrust law should reclaim its role as watchdog to stop abuses of economic power, and makes suggestions for U.S. antitrust law to meet the big-platform challenge in a modest but meaningful and practicable way. I. Introduction II. A Brief Comparison of U.S. and EU Law of Monopolization/Abuse of Dominance ... A. The United States ... B. Europe ... C. Presumptions and Divergences III. Implications for High Tech, Big Data IV. Three Examples of Alleged Platform Abuse ... A. Google/Comparative Shopping ... 1. EU Law ... 2. U.S. Law ... B. Facebook—Abuse of Data ... 1. German Law ... 2. U.S. Law ... C. Start-Ups: Nipping Competition in the Bud V. Proposals VI. Conclusion