Vision-language models (VLMs) have demonstrated impressive performance by effectively integrating visual and textual information to solve complex tasks. However, it is not clear how these models reason over the visual and textual data together, nor how the flow of information between modalities is structured. In this paper, we examine how VLMs reason by analyzing their biases when confronted with scenarios that present conflicting image and text cues, a common occurrence in real-world applications. To uncover the extent and nature of these biases, we build upon existing benchmarks to create five datasets containing mismatched image-text pairs, covering topics in mathematics, science, and visual descriptions. Our analysis shows that VLMs favor text in simpler queries but shift toward images as query complexity increases. This bias correlates with model scale, with the difference between the percentage of image- and text-preferred responses ranging from +56.8% (image favored) to -74.4% (text favored), depending on the task and model. In addition, we explore three mitigation strategies: simple prompt modifications, modifications that explicitly instruct models on how to handle conflicting information (akin to chain-of-thought prompting), and a task decomposition strategy that analyzes each modality separately before combining their results. Our findings indicate that the effectiveness of these strategies in identifying and mitigating bias varies significantly and is closely linked to the model's overall performance on the task and the specific modality in question.