Network Intrusion Detection Systems (NIDS) are a fundamental tool in cybersecurity. Their ability to generalize across diverse networks is a critical factor in their effectiveness and a prerequisite for real-world applications. In this study, we conduct a comprehensive analysis on the generalization of machine-learning-based NIDS through an extensive experimentation in a cross-dataset framework. We employ four machine learning classifiers and utilize four datasets acquired from different networks: CIC-IDS-2017, CSE-CIC-IDS2018, LycoS-IDS2017, and LycoS-Unicas-IDS2018. Notably, the last dataset is a novel contribution, where we apply corrections based on LycoS-IDS2017 to the well-known CSE-CIC-IDS2018 dataset. The results show nearly perfect classification performance when the models are trained and tested on the same dataset. However, when training and testing the models in a cross-dataset fashion, the classification accuracy is largely commensurate with random chance except for a few combinations of attacks and datasets. We employ data visualization techniques in order to provide valuable insights on the patterns in the data. Our analysis unveils the presence of anomalies in the data that directly hinder the classifiers capability to generalize the learned knowledge to new scenarios. This study enhances our comprehension of the generalization capabilities of machine-learning-based NIDS, highlighting the significance of acknowledging data heterogeneity.