Depth-integrated free-surface flow models are successfully applied in many geophysical applications like river floods, tsunami modeling, sediment transport or debris flows. In this talk, we want to compare the \textit{shear shallow flow} and the \textit{shallow moment} model. Both equations aim to extent the applicability of \textit{shallow water} model into an area where the vertical shear is not negligible and share some major aspects in their derivation. The methods are derived from the incompressible Euler or Navier-Stokes equations using similar scaling arguments combined with free-surface flow boundary conditions. The scaling results in a hydrostatic pressure law. Depth integration from the bottom topography ($h_b$) to the free surface ($h_s$) results in an unclosed system. Both approaches address this by splitting the velocity $\bm{u} = (u, v)^T$ into its mean $\bm{\bar{u}}$ and deviation $\bm{u}^d := \bm{u} - \bm{\bar{u}}$. The closure problem that now arises when integrating \begin{align}\label{eq:closureproblem} \int_{h_b}^{h_s} \bm{u} \otimes \bm{u} \; dz = \bm{\bar{u}} \otimes \bm{\bar{u}} + \underbrace{\int_{h_b}^{h_s} \left( \bm{\bar{u}} - \bm{u} \right) \otimes \left( \bm{\bar{u}} - \bm{u} \right) \; dz}_{=: \bm{P}_{ij}} \end{align} is solved by first applying the \textit{method of moments} to generate additional evolution equations. Here, the \textit{shear shallow flow} computes higher-order equations for the tensor $\bm{P}_{ij}$ and the system is closed by arguing that terms of higher order can be neglected based upon scaling arguments. The \textit{shallow moment} method on the other hand prescribes the shape of the velocity profile by expanding the deviatoric velocity profile $\bm{u}^d$ by using a Legendre basis, where each additional basis function generates an additional equation. The commonality between the models is their hierarchical approach to produce additional information to solve the closure problem \eqref{eq:closureproblem}, where the classical \text{shallow water} equations assumed $\bm{u}^d = \bm{0}$, resulting in a constant vertical velocity profile. A comparison of the models is presented based on geophysical relevant test cases and applications like a two-dimensional roll-wave example and the flow through an open-curved channel.