  We present a new approach to factorize and resum the post-Newtonian (PN)
waveform for generic equatorial motion to be used within effective-one-body
(EOB) based waveform models. The new multipolar waveform factorization improves
previous prescriptions in that: (i) the generic Newtonian contribution is
factored out from each multipole; (ii) the circular part is factored out and
resummed using standard EOB methods and (iii) the residual, 2PN-accurate,
noncircular part, and in particular the tail contribution, is additionally
resummed using Pad\'e approximants. The resulting waveform is validated in the
extreme-mass-ratio limit by comparisons with nine (mostly nonspinning)
numerical waveforms either from eccentric inspirals, with eccentricities up to
$e=0.9$, or dynamical captures . The resummation of the noncircular tail
contribution is found essential to obtain excellent (${\lesssim}0.05$~rad at
periastron for $e=0.9$) analytical/numerical agreement and to considerably
improve the prescription with just the Newtonian prefactor. In the comparable
mass case, the new 2PN waveform shows only a marginal improvement over the
previous Newtonian factorization, though yielding maximal unfaithfulness
$\simeq 10^{-3}$ with the 28 publicly available numerical relativity
simulations with eccentricity up to $\sim 0.3$ (except for a single outlier
that grazes $10^{-2}$). We finally use test-particle data to validate the
waveform factorization proposed by Khalil et al.~[Phys.~Rev.~104 (2021) 2,
024046] and conclude that its amplitude can be considered reliable (though less
accurate, $\sim 6\%$ fractional difference versus $1.5\%$ of our method) only
up to eccentricities $\sim 0.3$.
