Software defect prediction is a critical aspect of software quality assurance, as it enables early identification and mitigation of defects, thereby reducing the cost and impact of software failures. Over the past few years, quantum computing has risen as an exciting technology capable of transforming multiple domains; Quantum Machine Learning (QML) is one of them. QML algorithms harness the power of quantum computing to solve complex problems with better efficiency and effectiveness than their classical counterparts. However, research into its application in software engineering to predict software defects still needs to be explored. In this study, we worked to fill the research gap by comparing the performance of three QML and five classical machine learning (CML) algorithms on the 20 software defect datasets. Our investigation reports the comparative scenarios of QML vs. CML algorithms and identifies the better-performing and consistent algorithms to predict software defects. We also highlight the challenges and future directions of employing QML algorithms in real software defect datasets based on the experience we faced while performing this investigation. The findings of this study can help practitioners and researchers further progress in this research domain by making software systems reliable and bug-free.