3D free boundary equilibrium computations have recently been used to model external kinks and edge harmonic oscillations (EHOs), comparing with linear MHD stability codes, and nonlinear analytic theory [Kleiner et al., Phys. Plasma Controlled Fusion 61, 084005 (2019)]. In this study, results of the VMEC equilibrium code are compared further with nonlinear reduced MHD simulations, using the JOREK code. The purpose of this investigation was to understand the extent to which the modeling approaches agree, and identify the important physical effects, which can modify the dynamics. For the simulated external kink, which is dominated by a single toroidal harmonic, good agreement is found when a large Lundquist number is used in the JOREK simulation, such that resistive effects are sub-dominant. Modeling EHOs where multiple toroidal harmonics are linearly unstable, the saturated perturbation observed can differ in the dominant toroidal harmonic. On the ideal timescale, a n = 2 EHO is observed in JOREK, while the saturated perturbation predicted by VMEC is a n = 1 mode. Extending simulations into timescales where resistive effects can play a role, similar n = 1 perturbations can be found. The coupling of different linearly unstable toroidal harmonics in the JOREK simulation broadens the magnetic energy spectrum and ergodises the plasma edge region, resulting in a more localized pressure perturbation. These effects are not observed in VMEC, because closed magnetic flux surfaces are enforced. Despite the sensitivity of JOREK results on the assumed resistivity, saturated states can be found using both approaches that are in reasonable agreement, even for this more advanced case. Published under an exclusive license by AIP Publishing.