  We carry out a systematic study of collective spin- and charge excitations
for the canonical single-band Hubbard, $t$-$J$-$U$, and $t$-$J$ models of
high-temperature copper-oxide superconductors, both on electron- and hole-doped
side of the phase diagram. Recently developed variational wave function
approach, combined with the expansion in inverse number of fermionic flavors,
is employed. All three models exhibit a substantial electron-hole asymmetry of
magnetic excitations, with a robust paramagnon emerging for hole-doping, in
agreement with available resonant inelastic $x$-ray scattering data for the
cuprates. The $t$-$J$ model yields additional high-energy peak in the magnetic
spectrum that is not unambiguously identified in spectroscopy. For all
considered Hamiltonians, the dynamical charge susceptibility contains a
coherent mode for both hole- and electron doping, with overall bandwidth
renormalization controlled by the on-site Coulomb repulsion. Away from the
strong-coupling limit, the antiferromagnetic ordering tendency is more
pronounced on electron-doped side of the phase diagram.
