In this work, we performed a thorough comparative analysis on a radio frequency (RF) based drone detection and identification system (DDI) under wireless interference, such as WiFi and Bluetooth, by using machine learning algorithms, and a pre-trained convolutional neural network-based algorithm called SqueezeNet, as classifiers. In RF signal fingerprinting research, the transient and steady state of the signals can be used to extract a unique signature from an RF signal. By exploiting the RF control signals from unmanned aerial vehicles (UAVs) for DDI, we considered each state of the signals separately for feature extraction and compared the pros and cons for drone detection and identification. Using various categories of wavelet transforms (discrete wavelet transform, continuous wavelet transform, and wavelet scattering transform) for extracting features from the signals, we built different models using these features. We studied the performance of these models under different signal to noise ratio (SNR) levels. By using the wavelet scattering transform to extract signatures (scattergrams) from the steady state of the RF signals at 30 dB SNR, and using these scattergrams to train SqueezeNet, we achieved an accuracy of 98.9% at 10 dB SNR.