  The high energy neutrino cross section is a crucial ingredient in the
calculation of the event rate in high energy neutrino telescopes. Currently
there are several approaches which predict different behaviours for its
magnitude for ultrahigh energies. In this paper we present a comparison between
the predictions based on linear DGLAP dynamics, non-linear QCD and in the
imposition of a Froissart-like behaviour at high energies. In particular, we
update the predictions based on the Color Glass Condensate, presenting for the
first time the results for $\sigma_{\nu N}$ using the solution of the running
coupling Balitsky-Kovchegov equation. Our results demonstrate that the current
theoretical uncertainty for the neutrino-nucleon cross section reaches a factor
three for neutrinos energies around $10^{11}$ GeV and increases to a factor
five for $10^{13}$ GeV.
