Audio DeepFakes allow the creation of high-quality, convincing utterances and therefore pose a threat due to its potential applications such as impersonation or fake news. Methods for detecting these manipulations should be characterized by good generalization and stability leading to robustness against attacks conducted with techniques that are not explicitly included in the training. In this work, we introduce Attack Agnostic Dataset - a combination of two audio DeepFakes and one anti-spoofing datasets that, thanks to the disjoint use of attacks, can lead to better generalization of detection methods. We present a thorough analysis of current DeepFake detection methods and consider different audio features (front-ends). In addition, we propose a model based on LCNN with LFCC and mel-spectrogram front-end, which not only is characterized by a good generalization and stability results but also shows improvement over LFCC-based mode - we decrease standard deviation on all folds and EER in two folds by up to 5%.