We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\\it Saccharomyces cerevisiae} and compare them with a previously proposed ensemble of networks generated by mimicking the transcriptional regulation process within the cell. Even though the model ensemble successfully reproduces the degree distributions, degree-degree correlations and the k-core structure observed in Yeast, we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes. We use a Boolean model for the regulation dynamics and comment on the impact of various Boolean function classes that have been suggested to better represent in vivo regulatory interactions. In addition to an exceptionally large dynamical core network and an excess of self-intercting genes, we find that, even when these differences are eliminated, the Yeast accommodates more dynamical attractors than best matching model networks which typically come with a single dominant attractor. We further investigate the robustness of the networks under minor perturbations. We find that, requiring all inputs of the Boolean functions to be nonredundant squeezes the stability of the system to a narrower band near the order-chaos boundary, while the network stability still depends strongly on the used function class. The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core.