  We compare recently computed waveforms from second-order gravitational
self-force (GSF) theory to those generated by a new, GSF-informed, effective
one body (EOB) waveform model for (spin-aligned, eccentric) inspiralling black
hole binaries with large mass ratios. We focus on quasi-circular, nonspinning,
configurations and perform detailed GSF/EOB waveform phasing comparisons,
either in the time domain or via the gauge-invariant dimensionless function
$Q_\omega\equiv \omega^2/\dot{\omega}$, where $\omega$ is the gravitational
wave frequency. The inclusion of high-PN test-mass terms within the EOB
radiation reaction (notably, up to 22PN) is crucial to achieve an EOB/GSF
phasing agreement below 1~rad up to the end of the inspiral for mass ratios up
to 500. For larger mass ratios, up to $5\times 10^4$, the contribution of
horizon absorption becomes more and more important and needs to be accurately
modeled. Our results indicate that our GSF-informed EOB waveform model is a
promising tool to describe waveforms generated by either intermediate or
extreme mass ratio inspirals for future gravitational wave detectors
