Several studies of nearby active galactic nuclei (AGN) have shown that the soft X-ray emission presents a size and morphology that resembles that of the narrow-line region (NLR) traced by [O III]. Since the NLR is mainly constituted by gas photoionised by the AGN, it seems logical to assume that this is also the primary source of the soft X-ray emission. However, these results are based on individual sources or small samples, particularly focused on type-2 Seyfert galaxies. Very little has been said concerning other types of AGN. The purpose of this work is to compare the circumnuclear morphologies of soft X-ray and [O III] images to test whether they match in different optical classes of AGN. Our sample is composed of 27 AGN: nine type-1 Seyferts, 10 type-2 Seyferts, and eight low ionisation nuclear emission-line regions (LINERs). We find a good match in 100% of the type-2 Seyferts in our sample. This correspondence is less frequent in type-1 Seyferts (22%) and it is not seen in LINERs. The good resemblance in type-2 Seyferts constitutes an evidence for a common physical origin. We argue that the lack of correspondence in type-1 Seyferts might be due to the line of sight perpendicular to the accretion disk. Based on the morphologies of the eight LINERs in our sample, we discard a common origin for the soft X-ray and [O III] emissions in these objects. Regarding the X-ray properties, both high column density and hard X-ray luminosity are associated with matched morphologies.