Background: Static Application Security Testing (SAST) tools purport to assist developers in detecting security issues in source code. These tools typically use rule-based approaches to scan source code for security vulnerabilities. However, due to the significant shortcomings of these tools (i.e., high false positive rates), learning-based approaches for Software Vulnerability Prediction (SVP) are becoming a popular approach. Aims: Despite the similar objectives of these two approaches, their comparative value is unexplored. We provide an empirical analysis of SAST tools and SVP models, to identify their relative capabilities for source code security analysis. Method: We evaluate the detection and assessment performance of several common SAST tools and SVP models on a variety of vulnerability datasets. We further assess the viability and potential benefits of combining the two approaches. Results: SAST tools and SVP models provide similar detection capabilities, but SVP models exhibit better overall performance for both detection and assessment. Unification of the two approaches is difficult due to lacking synergies. Conclusions: Our study generates 12 main findings which provide insights into the capabilities and synergy of these two approaches. Through these observations we provide recommendations for use and improvement.