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The remarkable evolution of generative models has enabled the generation of high-quality, visually attractive images, often perceptually indistinguishable from real photographs to human eyes. This has spurred significant attention on AI-generated image (AIGI) detection. Intuitively, higher image quality should increase detection difficulty. However, our systematic study on cutting-edge text-to-image generators reveals a counterintuitive finding: AIGIs with higher quality scores, as assessed by human preference models, tend to be more easily detected by existing models. To investigate this, we examine how the text prompts for generation and image characteristics influence both quality scores and detector accuracy. We observe that images from short prompts tend to achieve higher preference scores while being easier to detect. Furthermore, through clustering and regression analyses, we verify that image characteristics like saturation, contrast, and texture richness collectively impact both image quality and detector accuracy. Finally, we demonstrate that the performance of off-the-shelf detectors can be enhanced across diverse generators and datasets by selecting input patches based on the predicted scores of our regression models, thus substantiating the broader applicability of our findings. Code and data are available at \href{https://github.com/Coxy7/AIGI-Detection-Quality-Paradox}{GitHub}.