This paper presents a comparative performance evaluation of energy detector (ED) under the assumption that the propagation signal experiences fading modeled by the nonlinear generalized alpha-kappa-mu or alpha-kappa-mu-Extreme fading channels. Novel closed-form analytical expressions for the average probability of detection and the average area under the receiver operating characteristic (ROC) curve (AUC) are derived in terms of the now highly prevalent bivariate Fox H-function under single-user spectrum sensing, cooperative spectrum sensing, and square law selection diversity reception. The results derived in the present work are generic as both channel models are compound distributions containing as special cases several other well-known fading models such as the Nakagami-m, Rice, the one-sided Gaussian distribution, and the Weibull distribution, among others. The performance of ED is evaluated by employing the traditional ROC and AUC curves over additive white Gaussian noise by varying model parameters and observing system performances. Analytical results are verified via Monte Carlo simulations in MATLAB (R).