  Lower-order $P_2$ finite elements are popular for solving fourth-order
elliptic PDEs when the solution has limited regularity. A priori and a
posteriori error estimates for von Karman equations are considered in
Carstensen et al. (2019, 2020) with respect to different mesh dependent norms
which involve different jump and penalization terms. This paper addresses the
question, whether they are comparable with respect to a common norm. This
article establishes that the errors for the quadratic symmetric interior
discontinuous Galerkin, $C^0$ interior penalty and nonconforming Morley finite
element methods are equivalent upto some higher-order oscillation term with
respect to a unified norm. Numerical experiments are performed to substantiate
the comparison results.
