Hyperspectral cameras onboard unmanned aerial vehicles (UAVs) have recently emerged for monitoring crop traits at the sub-field scale. Different physical, statistical, and hybrid methods for crop trait retrieval have been developed. However, spectra collected from UAVs can be confounded by various issues, including illumination variation throughout the crop growing season, the effect of which on the retrieval performance is not well understood at present. In this study, four retrieval methods are compared, in terms of retrieving the leaf area index (LAI), fractional vegetation cover (fCover), and canopy chlorophyll content (CCC) of potato plants over an agricultural field for six dates during the growing season. We analyzed: (1) The standard look-up table method (LUTstd), (2) an improved (regularized) LUT method that involves variable correlation (LUTreg), (3) hybrid methods, and (4) random forest regression without (RF) and with (RFexp) the exposure time as an additional explanatory variable. The Soil–Leaf–Canopy (SLC) model was used in association with the LUT-based inversion and hybrid methods, while the statistical modelling methods (RF and RFexp) relied entirely on in situ data. The results revealed that RFexp was the best-performing method, yielding the highest accuracies, in terms of the normalized root mean square error (NRMSE), for LAI (5.36%), fCover (5.87%), and CCC (15.01%). RFexp was able to reduce the effects of illumination variability and cloud shadows. LUTreg outperformed the other two retrieval methods (hybrid methods and LUTstd), with an NRMSE of 9.18% for LAI, 10.46% for fCover, and 12.16% for CCC. Conversely, LUTreg led to lower accuracies than those derived from RF for LAI (5.51%) and for fCover (6.23%), but not for CCC (16.21%). Therefore, the machine learning approaches—in particular, RF—appear to be the most promising retrieval methods for application to UAV-based hyperspectral data.