As deep neural networks are more commonly deployed in high-stakes domains, their lack of interpretability makes uncertainty quantification challenging. We investigate the effects of presenting conformal prediction sets$\unicode{x2013}$a method for generating valid confidence sets in distribution-free uncertainty quantification$\unicode{x2013}$to express uncertainty in AI-advised decision-making. Through a large online experiment, we compare the utility of conformal prediction sets to displays of Top-$1$ and Top-$k$ predictions for AI-advised image labeling. We find that the utility of prediction sets for accuracy varies with the difficulty of the task: while they result in accuracy on par with or less than Top-$1$ and Top-$k$ displays for easy images, prediction sets excel at assisting humans in labeling out-of-distribution (OOD) images especially when the set size is small. Our results empirically pinpoint the practical challenges of conformal prediction sets and provide implications on how to incorporate them for real-world decision-making.