In the literature, there are various simplifying assumptions adopted in the kinematic relations of the faces and the core when considering a geometrically nonlinear problem in sandwich structures. Most commonly, only one nonlinear term is included in the faces and the core nonlinearities are neglected. A critical assessment of these assumptions, as well as the effects of including the other nonlinear terms in the faces and the core, is the scope of this paper. The comprehensive investigation of all the nonlinear terms is accomplished by deriving and employing an advanced nonlinear high-order theory, namely, the recently developed “extended high-order sandwich panel theory” (EHSAPT). This theory, which was derived as a linear theory, is first formulated in this paper in its full nonlinear version for the simpler one-dimensional case of sandwich wide panels/beams. Large displacements and moderate rotations are taken into account in both faces and core. In addition, a nonlinear EHSAPT-based finite element (FE) is developed. A series of simplified models with various nonlinear terms included are derived accordingly to check the validity of each of these assumptions. Two sandwich panel configurations, one with a “soft” and one with a “hard” core, loaded in three-point bending, are analyzed. The geometric nonlinearity effects and the relative merits of the corresponding simplifications are analyzed with these two numerical examples. In addition to a relative comparison among all these different assumptions, the results are also compared to the corresponding ones from a commercial FE code.