This paper examines the competition between search engines and the implications of the EU Digital Markets Act (DMA) on user welfare. It also looks at the impact of generative AI models, such as Large Language Models (LLMs), chatbots and answer engines, on competition in search markets. The paper concludes that asymmetric data sharing may increase competition but may also reduce scale and user welfare, depending on the search-data learning curve. It also suggests policy recommendations to reduce tension between competition and welfare, including symmetric data sharing and user real-time search history and profile-data portability.