Spatial audio enhances immersion in applications such as virtual reality, augmented reality, gaming, and cinema by creating a three-dimensional auditory experience. Ensuring the spatial fidelity of binaural audio is crucial, given that processes such as compression, encoding, or transmission can alter localization cues. While subjective listening tests like MUSHRA remain the gold standard for evaluating spatial localization quality, they are costly and time-consuming. This paper introduces BINAQUAL, a full-reference objective metric designed to assess localization similarity in binaural audio recordings. BINAQUAL adapts the AMBIQUAL metric, originally developed for localization quality assessment in ambisonics audio format to the binaural domain. We evaluate BINAQUAL across five key research questions, examining its sensitivity to variations in sound source locations, angle interpolations, surround speaker layouts, audio degradations, and content diversity. Results demonstrate that BINAQUAL effectively differentiates between subtle spatial variations and correlates strongly with subjective listening tests, making it a reliable metric for binaural localization quality assessment. The proposed metric provides a robust benchmark for ensuring spatial accuracy in binaural audio processing, paving the way for improved objective evaluations in immersive audio applications.