  Recent high-energy data from Fermi-LAT on the diffuse gamma-ray background
have been used to set among the best constraints on annihilating TeV cold dark
matter candidates. In order to assess the robustness of these limits, we
revisit and update the calculation of the isotropic extragalactic gamma-ray
intensity from dark matter annihilation. The emission from halos with masses
$\geq10^{10}\,M_{\odot}$ provides a robust lower bound on the predicted
intensity. The intensity including smaller halos whose properties are
extrapolated from their higher mass counterparts is typically 5 times higher,
and boost from subhalos yields an additional factor ~1.5. We also rank the
uncertainties from all ingredients and provide a detailed error budget for
them. Overall, our fiducial intensity is a factor 5 lower than the one derived
by the Fermi-LAT collaboration in their latest analysis. This indicates that
the limits set on extragalactic dark matter annihilations could be relaxed by
the same factor. We also calculate the expected intensity for self-interacting
dark matter in massive halos and find the emission reduced by a factor 3
compared to the collisionless counterpart. The next release of the CLUMPY code
will provide all the tools necessary to reproduce and ease future improvements
of this prediction.
