  We study gravitational and test-field perturbations for the two possible
families of spherically symmetric black-hole mimickers that smoothly
interpolate between regular black holes and horizonless compact objects
accordingly to the value of a regularization parameter. One family can be
described by the Bardeen-like metrics, and the other by the Simpson-Visser
metric. We compute the spectrum of quasi-normal modes (QNMs) of these
spacetimes enlightening a common misunderstanding regarding this computation
present in the recent literature. In both families, we observe long-living
modes for values of the regularization parameter corresponding to ultracompact,
horizonless configurations. Such modes appear to be associated with the
presence of a stable photon sphere and are indicative of potential non-linear
instabilities. In general, the QNM spectra of both families display deviations
from the standard spectrum of GR singular BHs. In order to address the future
detectability of such deviations in the gravitational-wave ringdown signal, we
perform a preliminary study, finding that third generation ground-based
detectors might be sensible to macroscopic values of the regularization
parameter.
