Reference wind turbines (RWTs) that reflect the state-of-the-art of current wind energy technology are necessary in order to properly evaluate innovative methods in wind turbine design and evaluation. The International Energy Agency (IEA) Wind Technology Collaboration Platform (TCP) Task 37 has recently developed a new RWT geared towards offshore floating-foundation applications: the IEA Wind 15 MW. The model has been implemented in two aeroelastic codes, OpenFAST and HAWC2, based on an underlying common ontology. However, these toolchains result in slightly different structural parameters, and the two codes utilise different structural models. Thus, to increase the utility of the model, it is necessary to compare the aeroelastic responses. This paper compares aeroelastic loads calculated using different fidelities of the blade model in OpenFAST (ElastoDyn and BeamDyn) and HAWC2 (prismatic Timoshenko without torsion and Timoshenko with fully populated stiffness matrix), where both codes use the DTU Basic controller and the same turbulence boxes to reduce discrepancies. The aeroelastic responses to steady wind, step wind and turbulent wind (per IEC 61400-1 wind class IB) are considered. The results indicate a generally good agreement between the loads dominated by aerodynamic thrust and force, especially for the no-torsion blade models. Discrepancies were observed in other load channels, partially due to differences in the asymmetric loading of the rotor and partially due to differing closed-loop dynamics, and they will be the subject of future investigations.