We conduct a systematic comparison of technology cost forecasts produced by expert elicitation methods and model-based methods. Our focus is on energy technologies due to their importance for energy and climate policy. We assess the performance of several forecasting methods by generating probabilistic technology cost forecasts rooted at various years in the past and then comparing these with observed costs in 2019. We do this for six technologies for which both observed and elicited data are available. The model-based methods use either deployment (Wright's law) or time (Moore's law) to forecast costs. We show that, overall, model-based forecasting methods outperformed elicitation methods. Their 2019 cost forecast ranges contained the observed values much more often than elicitations, and their forecast medians were closer to observed costs. However, all methods underestimated technological progress in almost all technologies, likely as a result of structural change across the energy sector due to widespread policies and social and market forces. We also produce forecasts of 2030 costs using the two types of methods for 10 energy technologies. We find that elicitations generally yield narrower uncertainty ranges than model-based methods. Model-based 2030 forecasts are lower for more modular technologies and higher for less modular ones. Future research should focus on further method development and validation to better reflect structural changes in the market and correlations across technologies.