NeuroGaze is a novel Virtual Reality (VR) interface that integrates electroencephalogram (EEG) and eye tracking technologies to enhance user interaction within virtual environments (VEs). Diverging from traditional VR input devices, NeuroGaze allows users to select objects in a VE through gaze direction and cognitive intent captured via EEG signals. The research assesses the performance of the NeuroGaze system against conventional input devices such as VR controllers and eye gaze combined with hand gestures. The experiment, conducted with 20 participants, evaluates task completion time, accuracy, cognitive load through the NASA-TLX surveys, and user preference through a post-evaluation survey. Results indicate that while NeuroGaze presents a learning curve, evidenced by longer average task durations, it potentially offers a more accurate selection method with lower cognitive load, as suggested by its lower error rate and significant differences in the physical demand and temporal NASA-TLX subscale scores. This study highlights the viability of incorporating biometric inputs for more accessible and less demanding VR interactions. Future work aims to explore a multimodal EEG-Functional near-infrared spectroscopy (fNIRS) input device, further develop machine learning models for EEG signal classification, and extend system capabilities to dynamic object selection, highlighting the progressive direction for the use of Brain-Computer Interfaces (BCI) in virtual environments.