  Gamma-ray burst analyses at neutrino telescopes are typically based on
diffuse or stacked (i.e., aggregated) neutrino fluxes, because the number of
events expected from a single burst is small. The interpretation of aggregated
flux limits implies new systematics not present for a single burst, such as by
the integration over parameter distributions (diffuse fluxes), or by the low
statistics in small burst samples (stacked fluxes). We simulate parameter
distributions with a Monte Carlo method computing the spectra burst by burst,
as compared to a conventional Monte Carlo integration. With this approach, we
can predict the behavior of the flux in the diffuse limit as well as in low
statistics stacking samples, such as used in recent IceCube data analyses. We
also include the flavor composition at the detector (ratio between muon tracks
and cascades) into our considerations. We demonstrate that the spectral
features, such as a characteristic multi-peak structure coming from
photohadronic interactions, flavor mixing, and magnetic field effects, are
typically present even in diffuse neutrino fluxes if only the redshift
distribution of the sources is considered, with z \simeq 1 dominating the
neutrino flux. On the other hand, we show that variations of the Lorentz boost
can only be interpreted in a model-dependent way, and can be used as a model
discriminator. For example, we illustrate that the observation of spectral
features in aggregated fluxes will disfavor the commonly used assumption that
bursts with small Lorentz factors dominate the neutrino flux, whereas it will
be consistent with the hypothesis that the bursts have similar properties in
the comoving frame.
