The rapid adoption of generative AI-powered search engines like ChatGPT, Perplexity, and Gemini is fundamentally reshaping information retrieval, moving from traditional ranked lists to synthesized, citation-backed answers. This shift challenges established Search Engine Optimization (SEO) practices and necessitates a new paradigm, which we term Generative Engine Optimization (GEO). This paper presents a comprehensive comparative analysis of AI Search and traditional web search (Google). Through a series of large-scale, controlled experiments across multiple verticals, languages, and query paraphrases, we quantify critical differences in how these systems source information. Our key findings reveal that AI Search exhibit a systematic and overwhelming bias towards Earned media (third-party, authoritative sources) over Brand-owned and Social content, a stark contrast to Google's more balanced mix. We further demonstrate that AI Search services differ significantly from each other in their domain diversity, freshness, cross-language stability, and sensitivity to phrasing. Based on these empirical results, we formulate a strategic GEO agenda. We provide actionable guidance for practitioners, emphasizing the critical need to: (1) engineer content for machine scannability and justification, (2) dominate earned media to build AI-perceived authority, (3) adopt engine-specific and language-aware strategies, and (4) overcome the inherent "big brand bias" for niche players. Our work provides the foundational empirical analysis and a strategic framework for achieving visibility in the new generative search landscape.