The O III λλ 4959, 5007 lines are a useful proxy to test the kinematic of the narrow-line region (NLR) in active galactic nuclei (AGN). In AGN, and particularly in narrow-line Seyfert 1 galaxies (NLS1s) these lines often show few peculiar features, such as blue wings, often interpreted as outflowing component, and a shift − typically toward lower wavelengths − of the whole spectroscopic feature in some exceptional sources, the so-called blue outliers, which are often associated to strong winds. We investigated the incidence of these peculiarities in two samples of radio-emitting NLS1s, one radio-loud and one radio-quiet. We also studied a few correlations between the observational properties of the O III lines and those of the AGN. Our aim was to understand the difference between radio-quiet and radio-loud NLS1s, which may in turn provide useful information on the jet formation mechanism. We find that the NLR gas is much more perturbed in radio-loud than in radio-quiet NLS1s. In particular the NLR dynamics in γ-ray emitting NLS1s appears to be highly disturbed, and this might be a consequence of interaction with the relativistic jet. The less frequently perturbed NLR in radio-quiet NLS1s suggests instead that these sources likely do not harbor a fully developed relativistic jet. Nonetheless blue-outliers in radio-quiet NLS1s are observed, and we interpret them as a product of strong winds.