Reliable uncertainty quantification (UQ) is essential when employing large language models (LLMs) in high-risk domains such as clinical question answering (QA). In this work, we evaluate uncertainty estimation methods for clinical QA focusing, for the first time, on eleven clinical specialties and six question types, and across ten open-source LLMs (general-purpose, biomedical, and reasoning models), alongside representative proprietary models. We analyze score-based UQ methods, present a case study introducing a novel lightweight method based on behavioral features derived from reasoning-oriented models, and examine conformal prediction as a complementary set-based approach. Our findings reveal that uncertainty reliability is not a monolithic property, but one that depends on clinical specialty and question type due to shifts in calibration and discrimination. Our results highlight the need to select or ensemble models based on their distinct, complementary strengths and clinical use.