People increasingly rely on Artificial Intelligence (AI) based systems to aid decision-making in various domains and often face a choice between alternative systems. We explored the effects of users' perception of AI systems' warmth (perceived intent) and competence (perceived ability) on their choices. In a series of studies, we manipulated AI systems' warmth and competence levels. We show that, similar to the judgments of other people, there is often primacy for warmth over competence. Specifically, when faced with a choice between a high-competence system and a high-warmth system, more participants preferred the high-warmth system. Moreover, the precedence of warmth persisted even when the high-warmth system was overtly deficient in its competence compared to an alternative high competence-low warmth system. The current research proposes that it may be vital for AI systems designers to consider and communicate the system's warmth characteristics to its potential users.