Different formulations of finite elements with embedded strong discontinuities can be found in the literature. Jirasek et al. [1] present a classification and comparison of these elements. However, since the publication of the referred work, the formulation has evolved, then such comparison requires an update. In more recent studies, such as the one by Cazes et al. [2], even though it presented a comparison of the behavior of finite elements formulated with different versions of the Strong Discontinuity Approach, the authors limited their comparison by assuming only CST elements with a constant jump displacement field to describe the discontinuity. This work proposes to assess the behavior of different versions of embedded finite elements considering a broader set of possibilities. The investigation compares embedded strong discontinuity considering CST or linear quadrilateral elements, constant or linear jump displacement along the tangential discontinuity direction, and additional degrees of freedom that can be either global or statically condensed. The comparison is performed through a series of numerical examples in benchmark problems. The numerical results are compared against analytical solutions as well as solutions using interface elements. Finally, the investigation highlights the capabilities and limitations of each version of the embedded strong discontinuity approach.