Solid elements are aimed at modeling thick walled structures. As laminate thicknesses increase, out-of-plane stresses become more significant; Solid elements are better at approximating these effects. Furthermore, layered solid elements allow the incorporation of composite parts in larger solid model assemblies.
A shortcoming of these element types is that they are typically too stiff in bending when elements are thin. Displacements can be wrong by an order of magnitude as the elements undergo a phenomenon called locking. Element technologies such as Enhanced Strain Formulation try to remedy this numerical locking but are not sufficient to do so in linear 3D solid elements. Quadratic solid elements (SOLID186) offer a better solution, however, this comes at an increased computational cost.