People spend about 5-8 hours per day on phones, causing circadian disruption and eye fatigue, thus raising a great need for comfort and health. Most phones have eye protection modes, claiming a potential eye protection effect. To examine the effectiveness, we investigated the color quality, namely gamut area and just noticeable color difference (JNCD), and circadian effect, namely equivalent melanopic lux (EML) and melanopic daylight efficacy ratio (MDER), characteristics of two smartphones: iPhone 13 and HUAWEI P30, in normal and eye protection mode. The results show that the circadian effect is inversely proportional to color quality when the iPhone 13 and HUAWEI P30 changed from normal to eye protection mode. The gamut area changed from 102.51% to 82.5% sRGB and 100.36% to 84.55% sRGB, respectively. The EML and MDER decreased by 13 and 15, and, 0.50 and 0.38, respectively, affected by the eye protection mode and screen luminance. The EML and JNCD results in different modes show that the eye protection mode benefits the nighttime circadian effect at the cost of the image quality. This study provides a way to precisely assess the image quality and circadian effect of displays and elucidates the tradeoff relationship between them.