  Upcoming observational runs of the LIGO-Virgo-KAGRA collaboration, and future
gravitational-wave (GW) detectors on the ground and in space, require waveform
models more accurate than currently available. High-precision waveform models
can be developed by improving the analytical description of compact binary
dynamics and completing it with numerical-relativity (NR) information. Here, we
assess the accuracy of the recent results for the fourth post-Minkowskian (PM)
conservative dynamics through comparisons with NR simulations for the
circular-orbit binding energy and for the scattering angle. We obtain that the
4PM dynamics gives better agreement with NR than the 3PM dynamics, and that
while the 4PM approximation gives comparable results to the third
post-Newtonian (PN) approximation for bound orbits, it performs better for
scattering encounters. Furthermore, we incorporate the 4PM results in
effective-one-body (EOB) Hamiltonians, which improves the disagreement with NR
over the 4PM-expanded Hamiltonian from $\sim 40\%$ to $\sim 10\%$, or $\sim
3\%$ depending on the EOB gauge, for an equal-mass binary, two GW cycles before
merger. Finally, we derive a 4PN-EOB Hamiltonian for hyperbolic orbits, and
compare its predictions for the scattering angle to NR, and to the scattering
angle of a 4PN-EOB Hamiltonian computed for elliptic orbits.
