  The ringdown (RD) phase of gravitational waves is of prime interest for
testing general relativity (GR). The modelling of the linear quasi-normal modes
(QNMs) within the Kerr spectrum -- or with agnostic parameterized deviations to
that GR spectrum -- has become ordinary; however, specific attention has
recently emerged to calibrate the effects of nonlinear perturbations for the
predominant quadrupolar $l=2$, $m=2$ mode. In this paper, we test the
performance of a few nonlinear toy models and of the nonlinear
inspiral-merger-ringdown (IMR) model IMRPhenomD for faithfully representing the
RD regime and we compare them with the results obtained using linear solutions
as sums of QNM tones. Using several quasi-circular, non-precessing numerical
waveforms, we fit the dominant $l=2$, $m=2$ mode of the strain, and we assess
the results in terms of both the Bayes factor and the inferred posterior
distributions for the mass and spin of the final black hole (BH). We find that
the nonlinear models can be comparable or preferred over the linear QNM-only
solutions when the analysis is performed from the peak of the strain,
especially at high signal-to-noise ratios consistent with third-generation
observatories. Since the calibration of the tones' relative amplitudes and
phases in high-overtone models to the progenitor parameters is still missing,
or even not achievable, we consider the use of non-linear models to be more
pertinent for performing confident tests of general relativity based on the RD
regime starting from early times.
