Workplace negotiations are undermined by psychological barriers, which can even derail well-prepared tactics. AI offers personalized and always -- available negotiation coaching, yet its effectiveness for negotiation preparedness remains unclear. We built Trucey, a prototype AI coach grounded in Brett's negotiation model. We conducted a between-subjects experiment (N=267), comparing Trucey, ChatGPT, and a traditional negotiation Handbook, followed by in-depth interviews (N=15). While Trucey showed the strongest reductions in fear relative to both comparison conditions, the Handbook outperformed both AIs in usability and psychological empowerment. Interviews revealed that the Handbook's comprehensive, reviewable content was crucial for participants' confidence and preparedness. In contrast, although participants valued AI's rehearsal capability, its guidance often felt verbose and fragmented -- delivered in bits and pieces that required additional effort -- leaving them uncertain or overwhelmed. These findings challenge assumptions of AI superiority and motivate hybrid designs that integrate structured, theory-driven content with targeted rehearsal, clear boundaries, and adaptive scaffolds to address psychological barriers and support negotiation preparedness.