  We present accurate QCD predictions for the transverse momentum pT spectrum
of electroweak gauge bosons at the LHC for 13 TeV collisions, based on a
consistent combination of a NNLO calculation at large pT and N3LL resummation
in the small pT limit. The inclusion of higher order corrections leads to
substantial changes in the shape of the differential distributions, and the
residual perturbative uncertainties are reduced to the few percent level across
the whole transverse momentum spectrum. We examine the ratio of pT
distributions in charged- and neutral-current Drell-Yan production, and study
different prescriptions for the estimate of perturbative uncertainties that
rely on different degrees of correlation between these processes. We observe an
excellent stability of the ratios with respect to the perturbative order,
indicating a strong correlation between the corresponding QCD corrections.
