Dynamic models for credit rating transitions are important ingredients for dynamic credit risk analyses. We compare the properties of two such models that have recently been put forward. The models mainly differ in their treatment of systematic risk, which can be modeled either using discrete states (e.g., expansion versus recession) or continous states. It turns out that the implied asset correlations for discrete state switching models are implausibly low compared to correlation estimates in the literature. Given these limited correlations, we conclude that care has to be taken when discrete state regime switching models are employed for dynamic credit risk management. As a side result of our analysis, we obtain indirect evidence that default correlations may change over the business cycle.