We investigate the claim that the largest subhaloes in high resolution dissipationless cold dark matter (CDM) simulations of the Milky Way are dynamically inconsistent with observations of its most luminous satellites. We find that the inconsistency is largely attributable to the large values of sigma_8 and n_s adopted in the discrepant simulations producing satellites that form too early and therefore are too dense. We find the tension between observations and simulations adopting parameters consistent with WMAP9 is greatly diminished making the satellites a sensitive test of CDM. We find the Via Lactea II halo to be atypical for haloes in a WMAP3 cosmology, a discrepancy that we attribute to its earlier formation epoch than the mean for its mass. We also explore warm dark matter (WDM) cosmologies for 1--4 keV thermal relics. In 1 keV cosmologies subhaloes have circular velocities at kpc scales ~ 60% lower than their CDM counterparts, but are reduced by only 10% in 4 keV cosmologies. Since relic masses < 2-3 keV are ruled out by constraints from the number of Milky Way satellites and Lyman-alpha forest, WDM has a minor effect in reducing the densities of massive satellites. Given the uncertainties on the mass and formation epoch of the Milky Way, the need for reducing the satellite densities with baryonic effects or WDM is alleviated.
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