Compared to macro-econometric forecasting models, CGE models have a stronger foundation in economic theory. Macro-econometric forecasting models tend to be more data-driven, combining time series data with economic theory and often omit the detailed industrial data provided in CGE models.
I do not want to look like a Hidalgo Don Quichotte de la Mancha, and say that the CGE model is a typical model, since this model has its origins in the work of Léon Walras, and since I consider myself a Keynesian in thought and a new Keynesian in my analysis tools, I think this model in its first version (the Walrasian core) was less realistic! After the introduction of neoclassical assumptions and Arrow's concept of justice, I believe that the CGE model is a more realistic and practical model than econometric models, but econometric models still retain their macroeconomic importance!
At the end of all this and that, for me there is a question no less important than yours: mathematical modelling Vs. econometric modelling ?