Performance uncertainty quantification is essential for reliable validation and eventual clinical translation of medical imaging artificial intelligence (AI). Confidence intervals (CIs) play a central role in this process by indicating how precise a reported performance estimate is. Yet, due to the limited amount of work examining CI behavior in medical imaging, the community remains largely unaware of how many diverse CI methods exist and how they behave in specific settings. The purpose of this study is to close this gap. To this end, we conducted a large-scale empirical analysis across a total of 24 segmentation and classification tasks, using 19 trained models per task group, a broad spectrum of commonly used performance metrics, multiple aggregation strategies, and several widely adopted CI methods. Reliability (coverage) and precision (width) of each CI method were estimated across all settings to characterize their dependence on study characteristics. Our analysis revealed five principal findings: 1) the sample size required for reliable CIs varies from a few dozens to several thousands of cases depending on study parameters; 2) CI behavior is strongly affected by the choice of performance metric; 3) aggregation strategy substantially influences the reliability of CIs, e.g. they require more observations for macro than for micro; 4) the machine learning problem (segmentation versus classification) modulates these effects; 5) different CI methods are not equally reliable and precise depending on the use case. These results form key components for the development of future guidelines on reporting performance uncertainty in medical imaging AI.