Automatic summarization of legal case documents is an important and challenging problem, where algorithms attempt to generate summaries that match well with expert-generated summaries. This work takes the first step in analyzing expert-generated summaries and algorithmic summaries of legal case documents. We try to uncover how law experts write summaries for a legal document, how various generic as well as domain-specific extractive algorithms generate summaries, and how the expert summaries vary from the algorithmic summaries. We also analyze which important sentences of a legal case document are missed by most algorithms while generating summaries, in terms of the rhetorical roles of the sentences and the positions of the sentences in the legal document.