Fiber-reinforced laminates are vital in lightweight design due to their high stiffness-to-weight ratio and tunable properties. However, their anisotropic, inhomogeneous nature complicates the prediction of the behavior of fiber-reinforced laminate structures under loading. To address this challenge, various modeling approaches have been developed, balancing computational cost and accuracy. For component-level analyses, macro-scale models (using a homogenized material) are typically the most computationally feasible. These range from efficient Reissner-Mindlin shell elements to fully three-dimensional simulations with stacked solid elements. For larger-scale simulations, using solid elements stacked in the laminate thickness direction is computationally prohibitive. In this case, Reissner-Mindlin shell elements are preferred for their efficiency, but they only consider a reduced stress state. Indeed, in certain laminate analyses, considering a fully three-dimensional stress state is crucial; for example, for plates in localized regions of complex loading (Kamis, 2012) or geometry or close to free edges of laminates (Dhanesh et al., 2017). To enhance stress prediction, Schilling et al. (2024, in publication) investigated the option of using higher-order 3D-shell elements in comparison to standard shell elements. These higher-order 3D-shell elements account for a warping deformation of cross-sectional fibers and a non-homogeneous thickness stretch, enabling the prediction of a fully three-dimensional stress state. Building on this work, we analyze a broader range of scenarios, including more complex laminates and the effects of damage. We compare higher-order 3D-shell elements with Reissner-Mindlin shell elements and shell elements with constant thickness stretch, all using a fully anisotropic material model. Simulations with stacked solid elements serve as reference. We conclude that higher-order 3D-shell elements significantly improve stress prediction and offer potential benefits for damage prediction for fiber-reinforced laminates while maintaining computational efficiency. This research is supported by the DigiTain project (19S22006K), funded by the Federal Ministry of Economic Affairs and Climate Action, following on a resolution of the German Bundestag.