A broad range of supervised Machine Learning and parametric statistical, geospatial and non-geospatial models are applied to model both aggregated observed impact estimate count data and satellite image-derived geo-located building damage labelled data, via regression- and classification-based models, respectively. For the former, models are ranked via predictive performance of mortality, population displacement, building damage and building destruction for 161 earthquakes in 61 countries. For the latter, models were ranked via classification performance (damaged/unaffected) of 369,813 geo-located buildings for 26 earthquakes in 15 countries. k-fold, 3-repeat cross validation is utilised to ensure out-of-sample predictive performance. Feature importance on several variables used as proxies for disaster-risk vulnerability indicates covariate utility. The 2023 Türkiye-Syria earthquakes event is shown to be unlike any of the other 161 earthquakes, resulting in high prediction error for the aggregated impact models compared to all other events, reflecting model limitations on extreme events. However, training the building damage classifier AdaBoost model on all except the 2023 Türkiye-Syria earthquakes, predictions on the 27,032 held-out buildings have an AUC of 0.93. Therefore, without any geospatial, building-specific or direct satellite image information, this model accurately classifies building damage, with significantly improved performance over satellite-image trained models found in the literature.