Miniaturised hyperspectral cameras are becoming more easily accessible and smaller, enabling efficient monitoring of agricultural crops using unoccupied aerial systems (UAS). This study’s objectives were to develop and assess the performance of UAS-based hyperspectral cameras in the estimation of quantity and quality parameters of grass sward, including the fresh and dry matter yield, the nitrogen concentration (Ncont) in dry matter (DM), the digestibility of organic matter in DM (the D-value), neutral detergent fibre (NDF), and water-soluble carbohydrates (WSC). Next-generation hyperspectral cameras in visible-near-infrared (VNIR, 400–1000 nm; 224 bands) and shortwave-infrared (SWIR; 900–1700 nm; 224 bands) spectral ranges were used, and they were compared with commonly used RGB and VNIR multispectral cameras. The implemented machine-learning framework identified the most informative predictors of various parameters, and estimation models were then built using a random forest (RF) algorithm for each camera and its combinations. The results indicated accurate estimations; the best normalised root-mean-square errors (NRMSE) were 8.40% for the quantity parameters, and the best NRMSEs for the quality parameters were 7.44% for Ncont, 1% for D-value, 1.24% for NDF, and 12.02% for WSC. The hyperspectral datasets provided the best results, whereas the worst accuracies were obtained using the crop height model and RGB data. The integration of the VNIR and SWIR hyperspectral cameras generally provided the highest accuracies. This study showed for the first time the performance of novel SWIR range hyperspectral UAS cameras in agricultural application.