  The demonstration of superconductivity in nickelate analogues of high $T_c$
cuprates provides new perspectives on the physics of correlated electron
materials. The degree to which the nickelate electronic structure is similar to
that of cuprates is an important open question. This paper presents results of
a comparative study of the many-body electronic structure and theoretical phase
diagram of the isostructural materials CaCuO$_2$ and NdNiO$_2$. Important
differences include the proximity of the oxygen $2p$ bands to the Fermi level,
the bandwidth of the transition metal-derived $3d$ bands, and the presence, in
NdNiO$_2$, of both Nd-derived $5d$ states crossing the Fermi level and a van
Hove singularity that crosses the Fermi level as the out of plane momentum is
varied. The low energy physics of NdNiO$_2$ is found to be that of a single
Ni-derived correlated band, with additional accompanying weakly correlated
bands of Nd-derived states that dope the Ni-derived band. The effective
correlation strength of the Ni-derived $d$-band crossing the Fermi level in
NdNiO$_2$ is found to be greater than that of the Cu-derived $d$-band in
CaCuO$_2$, but the predicted magnetic transition temperature of NdNiO$_2$ is
substantially lower than that of CaCuO$_2$ because of the smaller bandwidth.
