In designing and evaluating human-robot interactions and interfaces, researchers often use a simulated robot due to the high cost of robots and time required to program them. However, it is important to consider how interaction with a simulated robot differs from a real robot; that is, do simulated robots provide authentic interaction? We contribute to a growing body of work that explores this question and maps out simulated-versus-real differences, by explicitly investigating empathy: how people empathize with a physical or simulated robot when something bad happens to it. Our results suggest that people may empathize more with a physical robot than a simulated one, a finding that has important implications on the generalizability and applicability of simulated HRI work. Empathy is particularly relevant to social HRI and is integral to, for example, companion and care robots. Our contribution additionally includes an original and reproducible HRI experimental design to induce empathy toward robots in laboratory settings, and an experimentally validated empathy-measuring instrument from psychology for use with HRI.