There is vivid research on adapting Large Language Models (LLMs) to perform a variety of tasks in high-stakes domains such as healthcare. Despite their popularity, there is a lack of understanding of the extent and contributing factors that allow LLMs to recall relevant knowledge and combine it with presented information in the clinical and biomedical domain: a fundamental pre-requisite for success on down-stream tasks. Addressing this gap, we use Multiple Choice and Abstractive Question Answering to conduct a large-scale empirical study on 22 datasets in three generalist and three specialist biomedical sub-domains. Our multifaceted analysis of the performance of 15 LLMs, further broken down by sub-domain, source of knowledge and model architecture, uncovers success factors such as instruction tuning that lead to improved recall and comprehension. We further show that while recently proposed domain-adapted models may lack adequate knowledge, directly fine-tuning on our collected medical knowledge datasets shows encouraging results, even generalising to unseen specialist sub-domains. We complement the quantitative results with a skill-oriented manual error analysis, which reveals a significant gap between the models' capabilities to simply recall necessary knowledge and to integrate it with the presented context. To foster research and collaboration in this field we share M-QALM, our resources, standardised methodology, and evaluation results, with the research community to facilitate further advancements in clinical knowledge representation learning within language models.