Previous studies have discouraged the use of the Cox proportional hazards (PH) model for traditional mediation analysis as it might provide biased results. Accelerated failure time (AFT) models have been proposed as an alternative for Cox PH models. In addition, the use of the potential outcomes framework has been proposed for mediation models with time-to-event outcomes. The aim of this paper is to investigate the performance of traditional mediation analysis and potential outcomes mediation analysis based on both the Cox PH and the AFT model. This is done by means of a Monte Carlo simulation study and the illustration of the methods using an empirical data set. Both the product-of-coefficients method of the traditional mediation analysis and the potential outcomes framework yield unbiased estimates with respect to their own underlying indirect effect value for simple mediation models with a time-to-event outcome and estimated based on Cox PH or AFT.