This paper analyzes firms competing to provide accurate model predictions in the AI model market and consumers who exhibit heterogeneous preferences for model accuracy. We develop a consumer-firm duopoly model to analyze the impact of competition on firms' incentives to improve model accuracy. While each firm seeks to minimize model error, this choice may not be optimal. Counterintuitively, we find that in a competitive market, improving overall accuracy does not necessarily improve profits. Instead, the optimal decision for each firm is to invest more in the error dimension where it has a competitive advantage. By decomposing model error into false positive and false negative rates, firms can reduce errors in each dimension through investment. Investing in the advantage dimension is strictly better for firms, while investing in the disadvantage dimension is strictly worse. While profitable investments negatively impact consumers, they increase overall welfare.