Automatic Modulation Classification (AMC) is an approach to identify an observed signal's most likely modulation scheme without any a priori knowledge of the intercepted signal. In this research, the authors present a new direction for both stages of feature-based (FB) approach. In the feature extraction stage, the authors design a new architecture that 1) removes the bias issue for the estimator of fourth-order cumulants, and 2) extracts polar-transformed information of the received IQ symbols, and finally 3) forms a unique dataset to be used in the labeling stage. Furthermore, the authors contribute to increasing the classification accuracy in low signal-to-noise ratio (SNR) conditions by employing the deep belief network (DBN) platform in addition to the spiking neural network (SNN) platform to overcome execution latency concerns associated with deep learning architectures. For this research, the authors first study each individual FB AMC classifier to derive their respective upper and lower performance bounds and then propose an adaptive framework that is built and developed with these findings. This framework aims to efficiently classify the modulation scheme by intelligently switching between these different FB classifiers to achieve an optimal balance between accuracy and execution latency for any observed channel conditions derived from the main receiver's equalizer. Subsequently, a performance analysis is conducted using the standard RadioML dataset to achieve a realistic evaluation. Numerical results indicate a notably higher classification accuracy, by 16.02% on average, when DBN is employed, whereas SNN requires significantly lower execution latency to label the modulation scheme when compared against two other modified FB classifiers that are built upon convolutional and recurrent neural networks, shown to be reduced by 34.31%.