Across all fields, respected experts cite their sources. While large language models (LLMs) excel at synthesizing information, they do not reliably cite sources, making it difficult to verify provided information. In contrast, search engines make sources readily accessible but burden users with synthesizing information. To rigorously examine the interplay between verifiability and utility, we build on classic theories of abstraction to propose an extractive-abstractive spectrum for cited generations; we define five operating points that span the extreme endpoints of extractive search engine outputs and abstractive LLM generations without reliable citation. We perform an analysis of the drawbacks and benefits of seven systems across the spectrum in the QA settings of search queries, information simplification, multi-hop reasoning, and health advice. As outputs become more abstractive, our human evaluations find that the proportion of properly cited sentences decreases by as much as 50%. Simultaneously, perceived utility improves by as much as 200% and users take up to 3 times as long to verify cited information. We recommend operating points for specific task settings and our failure analysis informs methods for citation identification, information retrieval, and multi-operating point systems.