Artificial intelligence (AI) coaching chatbots are increasingly used to support personal and professional development, yet little is known about how different coaching models translate into AI-mediated practice. This study compares three established coaching approaches: GROW, Solution Focused (SF), and Cognitive Behavioral Therapy (CBT) as implemented in generative AI chatbots. Drawing on Self-Determination Theory (SDT) and Transformative Learning Theory (TLT), we examine how these approaches influence three outcomes central to coaching: goal attainment, working alliance (bond, goal, task), and client perceptions of the coaching experience. In a two-wave experimental study (N = 592), participants were randomly assigned to engage with one of the three coaching chatbots over two sessions. Contrary to expectations derived from human coaching literature, the CBT-based chatbot outperformed both GROW and SF chatbots across most measures, suggesting that AI-mediated coaching may activate different psychological processes than human coaching. These findings extend coaching theory by exploring how established models function in AI contexts and highlight implications for coaching practice, training, and the integration of AI into organizational and developmental settings. The study also raises critical questions about the unique contribution of human coaches in an era of increasingly capable AI coaching tools.