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 Pade 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 (less than or similar to 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 similar or equal to 10(-3) with the 28 publicly available numerical relativity simulations with eccentricity up to similar to 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, 024046 (2021)] and conclude that its amplitude can be considered reliable (though less accurate, similar to 6% fractional difference versus 1.5% of our method) only up to eccentricities similar to 0.3.