This paper asks whether moral preferences in eight medical dilemmas change as a function of how preferences are expressed, and how people choose when they are faced with two equally attractive help projects. In two large-scale studies, participants first read dilemmas where they "matched" two suggested helping projects (which varied on a single attribute) so that they became equally attractive. They did this by filling in a missing number (e.g., how many male patients must Project M save in order to be equally attractive as Project F which can save 100 female patients). Later, the same participants were asked to choose between the two equally attractive projects. We found robust evidence that people do not choose randomly, but instead tend to choose projects that help female (vs. male), children (vs. adult), innocent (vs. non-innocent), in group (vs. outgroup) and existing (vs. future) patients, and imply no (vs. some) risk of a harmful side-effect, even when these projects have been matched as equally attractive as, and save fewer patients than the contrasting project. We also found that some moral preferences are hidden when expressed with matching but apparent when expressed with forced choice. For example, 88-95% of the participants expressed that female and male patients are equally valuable when doing the matching task, but over 80% of them helped female patients in the choice task.