The desire to understand and model the complex phenomenon of economic growth has been an old and interesting pursuit. Many such models have been proposed and two of the most prominent canditates are the Solow-Swan and Romer models. This paper investigates the similarities and differences of the a priori mentioned models on a balanced growth path and on a partial transition dynamics - only the capital dynamics - using numerical simulations. Furthermore, the problem of the speed of convergence shall be analyzed and a method for the analysis will be presented. The simulations are investigated by means of different economic scenarios, called experiments, and are used to illustrate the capabilities and incapabilities of each model. The findings of this paper are that both models are adequate for the investigation of economic growth. However, as seen by the mathematical analysis and the experiments, the incapability of the Solow-Swan model to adequately explain the technological growth rate is a strong disadvantage over the more modern Romer model. Furthermore, this paper summarizes the choices of the numerical values - using real world data - which should be used for the variables of the Solow-Swan and Romer models.