  We present an updated version of the TEOBResumS-Dali effective-one-body (EOB)
waveform model for spin aligned binaries on non-circularized orbits. Recently
computed 4PN (nonspinning) terms are incorporated in the waveform and radiation
reaction. The model is informed by a restricted sample ($\sim60$) of
spin-aligned, quasi-circular, Numerical Relativity (NR) simulations. In the
quasi-circular limit, the model displays EOB/NR unfaithfulness ${\bar{\cal
F}}^{\rm max}_{\rm EOBNR}\lesssim 10^{-2}$ (with median~ $1.06\times 10^{-3}$)
(with Advanced LIGO noise and in the total mass range $10-200M_\odot$) for the
dominant $\ell=m=2$ mode all over the 534 spin-aligned configurations available
through the Simulating eXtreme Spacetime catalog of NR waveforms. Similar
figures are also obtained with the 28 public eccentric SXS simulations and good
compatibility between EOB and NR scattering angles is found. The quasi-circular
limit of TEOBResumS-Dali is also found to be highly consistent with the
TEOBResumS-GIOTTO quasi-circular model. We then systematically explore the
importance of NR-tuning {\it also} the radiation reaction of the system. When
this is done, the median of the distribution of quasi-circular ${\bar{\cal
F}}^{\rm max}_{\rm EOBNR}$ is lowered to $3.92\times 10^{-4}$, though balanced
by a tail up to $\sim 0.1$ for large, positive spins. The same is true for the
eccentric-inspiral datasets. We conclude that an improvement of the analytical
description of the spin-dependent flux (and its interplay with the conservative
part) is likely to be the cornerstone to lower the EOB/NR unfaithfulness below
the $10^{-4}$ level all over the parameter space, thus grazing the current NR
uncertainties as well as the expected needs for next generation of GW detector
like Einstein Telescope.
