  The majority of known asteroid diameters are derived from thermal-infrared
observations. Diameters are derived using asteroid thermal models that
approximate their surface temperature distributions and compare the measured
thermal-infrared flux with model-dependent predictions. The most commonly used
thermal model is the Near-Earth Asteroid Thermal Model (NEATM), which is
usually perceived as superior to other models like the Fast-Rotating Model
(FRM). We investigate the applicability of the NEATM and the FRM to
thermal-infrared observations of Near-Earth Objects using synthetic asteroids
with properties based on the real Near-Earth Asteroid (NEA) population. We find
the NEATM to provide more accurate diameters and albedos than the FRM in most
cases, with a few exceptions. The modeling results are barely affected by the
physical properties of the objects, but we find a large impact of the solar
phase angle on the modeling results. We conclude that the NEATM provides
statistically more robust diameter estimates for NEAs observed at solar phase
angles less than ~65{\deg}, while the FRM provides more robust diameter
estimates for solar phase angles greater than ~65{\deg}. We estimate that <5%
of all NEA diameters and albedos derived up to date are affected by systematic
effects that are of the same order of magnitude as the typical thermal model
uncertainties. We provide statistical correction functions for diameters and
albedos derived using the NEATM and FRM as a function of solar phase angle.
