  Context. The large quantity of high-quality asteroseismic data that obtained
from space-based photometric missions and the accuracy of the resulting
frequencies motivate a careful consideration of the accuracy of computed
oscillation frequencies of stellar models, when applied as diagnostics of the
model properties.
  Aims. Based on models of red-giant stars that have been independently
calculated using different stellar evolution codes, we investigate the extent
to which the differences in the model calculation affect the model oscillation
frequencies.
  Methods. For each of the models, which cover four different masses and
different evolution stages on the red-giant branch, we computed full sets of
low-degree oscillation frequencies using a single pulsation code and, from
these frequencies, typical asteroseismic diagnostics. In addition, we carried
out preliminary analyses to relate differences in the oscillation properties to
the corresponding model differences.
  Results. In general, the differences in asteroseismic properties between the
different models greatly exceed the observational precision of these
properties, in particular for the nonradial modes whose mixed acoustic and
gravity-wave character makes them sensitive to the structure of the deep
stellar interior. In some cases, identifying these differences led to
improvements in the final models presented here and in Paper I; here we
illustrate particular examples of this.
  Conclusions. Further improvements in stellar modelling are required in order
fully to utilise the observational accuracy to probe intrinsic limitations in
the modelling. However, our analysis of the frequency differences and their
relation to stellar internal properties provides a striking illustration of the
potential of the mixed modes of red-giant stars for the diagnostics of stellar
interiors.
