In this work, we focus on a comparative study between the Representative Crack Element approach and the Star-convex formulation within phase-field fracture. This includes the one-dimensional discussion regarding tension–compression asymmetric behaviors, the comparison in terms of analytical elastic domains at certain damage levels in multi-axial case, and numerical simulations within finite element framework considering various scenarios. Of particular interest are the post-fracture mechanical behavior under complex loading cases, the mixed-mode fracture in comparison to analytical solutions, and the splitting cracks of ring Brazilian discs induced by compression. With this study, we reveal several fundamental and important characteristics of the considered approaches.