Modellers are increasingly relying on the use of continuous random coefficients models, such as Mixed Logit, for the representation of variations in tastes across individuals. In this paper, we provide an in-depth comparison of the performance of the Mixed Logit model with that of its far less commonly used discrete mixture counterpart, making use of a combination of real and simulated datasets. The results not only show significant computational advantages for the discrete mixture approach, but also highlight greater flexibility, and show that, across a host of scenarios, the discrete mixture models are able to offer comparable or indeed superior model performance.