The release frequency of software projects has increased in recent years. Adopters of so-called rapid release cycles claim that they can deliver addressed issues (i.e., bugs, enhancements, and new features) to users more quickly. However, there is little empirical evidence to support these claims. In fact, in our prior work, we found that code integration phases may introduce delays in rapidly releasing software - 98% of addressed issues in the rapidly releasing Firefox project had their integration delayed by at least one release. To better understand the impact that rapid release cycles have on the integration delay of addressed issues, we perform a comparative study of traditional and rapid release cycles. Through an empirical study of 72,114 issue reports from the Firefox system, we observe that, surprisingly, addressed issues take a median of 50 days longer to be integrated in rapid Firefox releases than the traditional ones. To investigate the factors that are related to integration delay in traditional and rapid release cycles, we train regression models that explain if an addressed issue will have its integration delayed or not. Our explanatory models achieve good discrimination (ROC areas of 0.81-0.83) and calibration scores (Brier scores of 0.05-0.16). Deeper analysis of our explanatory models indicates that traditional releases prioritize the integration of backlog issues, while rapid releases prioritize issues that were addressed during the current release cycle. Our results suggest that rapid release cycles may not be a silver bullet for the rapid delivery of addressed issues to users.