We make a quantitative comparison between spectral vs filter measurement and analysis techniques for extraction of solar vector magnetic fields from polarimetric data using as a basis the accurately calibrated, high angular resolution. Stokes profile data from the Advanced Stokes Polarimeter. It is shown that filter-based measurements deliver qualitative images of the field alignment for sunspots that are visually similar to images derived from the more detailed analysis of the Stokes profiles. However, quantitative comparison with least-squares fits to the full Stokes profiles show that both the strength of the field predicted by the filter-based analysis and its orientation contain substantial errors. These errors are largest for plage regions outside of sunspots, where the field strengths are inferred to be only a fraction of their true values, and errors in the orientation of 40-50 deg are common. Within sunspots, errors of 20 deg are commonplace. The greatest source of these errors is the inability of the filter-based measurements to account for the small fill fraction of magnetic fields, or, equivalently, scattered light in the instrument, which reduce the degree of polarization. The uncertainties of the full profile fitting methods are also discussed, along with the errors introduced by coarser wavelength sampling of the observed Stokes profiles. The least-squares fitting procedure operates best when the profiles are sampled at least as frequently as one Doppler width of the line.