<p>We develop methods for comparing solar active region magnetic fields using two forms of mode analysis. These methods are designed to directly compare all three field components of the magnetic field and characterise their differences in a manner that is both meaningful and interpretable. The first mode decomposition is a Zernike polynomial analysis, the planar counterpart of a spherical polar decomposition, used to compare the spectral properties of the fields at both small and large scales, as well as to assess the dominance of particular modes (bipolar/quadrupolar). The second method is a multi-resolution (wavelet) analysis, which allows one to precisely quantify the spatial variation between the fields. In this study, we use these decompositions to compare and contrast magnetogram data derived from convective flux emergence experiments with observed active-region data, in order to assess their viability as models of active-region formation. We show that both elements: a significant contribution from the rise through the convective zone in the model, and the choice of initial condition, play a key role in simulations accurately recreating the spectral properties of active region fields.</p>