The increasing availability of sensor data at machine tools makes automatic chatter detection algorithms a trending topic in metal cutting. Two prominent and advanced methods for feature extraction via signal decomposition are Wavelet Packet Transform (WPT) and Ensemble Empirical Mode Decomposition (EEMD). We apply these two methods to time series acquired from an acceleration sensor at the tool holder of a lathe. Different turning experiments with varying dynamic behavior of the machine tool structure were performed. We compare the performance of these two methods with Support Vector Machine (SVM), Logistic Regression, Random Forest Classification and Gradient Boosting combined with Recursive Feature Elimination (RFE). We also show that the common WPT-based approach of choosing wavelet packets with the highest energy ratios as representative features for chatter does not always result in packets that enclose the chatter frequency, thus reducing the classification accuracy. Further, we test the transfer learning capability of each of these methods by training the classifier on one of the cutting configurations and then testing it on the other cases. It is found that when training and testing on data from the same cutting configuration both methods yield high accuracies reaching in one of the cases as high as 94% and 95%, respectively, for WPT and EEMD. However, our experimental results show that EEMD can outperform WPT in transfer learning applications with accuracy of up to 95%.