Polynomial chaos and Gaussian process emulation are methods for surrogate-based uncertainty quantification, and have been developed independently in their respective communities over the last 25 years. Despite tackling similar problems in the field, to our knowledge there has yet to be a critical comparison of the two approaches in the literature. We begin by providing a detailed description of polynomial chaos and Gaussian process approaches for building a surrogate model of a black-box function. The accuracy of each surrogate method is then tested and compared for two simulators used in industry: a land-surface model (adJULES) and a launch vehicle controller (VEGACONTROL). We analyse surrogates built on experimental designs of various size and type to investigate their performance in a range of modelling scenarios. Specifically, polynomial chaos and Gaussian process surrogates are built on Sobol sequence and tensor grid designs. Their accuracy is measured by their ability to estimate the mean, standard deviation, exceedance probabilities and probability density function of the simulator output, as well as a root mean square error metric, based on an independent validation design. We find that one method does not unanimously outperform the other, but advantages can be gained in some cases, such that the preferred method depends on the modelling goals of the practitioner. Our conclusions are likely to depend somewhat on the modelling choices for the surrogates as well as the design strategy. We hope that this work will spark future comparisons of the two methods in their more advanced formulations and for different sampling strategies.