Background: Manually labeling sleep stages is time-consuming and labor-intensive, making automatic sleep staging methods crucial for practical sleep monitoring. While both single- and multi-channel data are commonly used in automatic sleep staging, limited research has adequately investigated the differences in their effectiveness. Methods: In this study, four public data sets—Sleep-SC, APPLES, SHHS1, and MrOS1—are utilized, and an advanced hybrid attention neural network composed of a multi-branch convolutional neural network and the multi-head attention mechanism is employed for automatic sleep staging. Results: The experimental results show that, for sleep staging using 2–5 classes, a combination of single-channel electroencephalography (EEG) and dual-channel electrooculography (EOG) consistently outperforms single-channel EEG with single-channel EOG, which in turn outperforms single-channel EEG or single-channel EOG alone. For instance, for five-class sleep staging using the MrOS1 data set, the combination of single-channel EEG and dual-channel EOG resulted in an accuracy of 87.18%, whereas the combination of single-channel EEG and single-channel EOG yielded an accuracy of 85.77%. In comparison, single-channel EEG alone achieved an accuracy of 85.25% and single-channel EOG alone achieved an accuracy of 83.66%. Conclusions: This study highlights the significance of combining EEG and EOG signals in automatic sleep staging, while also providing valuable insights for the channel design of portable sleep monitoring devices.