  We perform a comparative $2 \times 2$ real space cluster DMFT study on
minimal models for NdNiO$_2$ and CaCuO$_2$ obtained from downfolding DFT
states, using a Nambu formalism that allows for both superconducting and
antiferromagnetic order. We produce a phase diagram in temperature and doping.
We find that for the nickelate, like the cuprate, the stoichiometric compound
is antiferromagnetic. We find superconductivity in a doping range bounded, with
a small coexistence region, by the onset of antiferromagnetism at low doping
and with transition temperature becoming immeasurably small at high doping.
Superconductivity emerges at around the same hole doping for both compounds,
but requires a larger deviation from half filling for the nickelate. Both
antiferromagnetic and superconducting order lead to a partial gapping of the
$d_{x^2-y^2}$ Fermi surface sheet. Our similar results for the cuprate and
nickelate suggest that nickelate superconductivity is cupratelike. We compare
our results to the experimental phase diagram.
