We compare the apparent axial ratio distributions of the brightest cluster galaxies (BCGs) and normal ellipticals (Es) in our sample of 75 galaxy clusters from the WIde-field Nearby Galaxy-cluster Survey (WINGS). Most BCGs in our clusters (69 per cent) are classified as cD galaxies. The sample of cDs has been completed by 14 additional cDs (non-BCGs) we found in our clusters. We deproject the apparent axial ratio distributions of Es, BCGs and cDs using a bivariate version of the Lucy rectification algorithm, whose results are supported by an independent Monte Carlo technique. Finally, we compare the intrinsic shape distribution of BCGs to the corresponding shape distribution of the central part of cluster-sized dark matter haloes extracted from the GIF2 Lambda cold dark matter (ΛCDM) N-body simulations (Gao et al.). We find that (i) Es have triaxial shape, the triaxiality sharing almost evenly the intrinsic axial ratio parameter space, with a weak preference for prolateness and (ii) the BCGs have triaxial shape as well. However, their tendency towards prolateness is much stronger than in the case of Es. Such a strong prolateness appears entirely due to the sizeable (dominant) component of cDs inside the WINGS sample of BCGs. In fact, while the `normal' (non-cD) BCGs do not differ from Es, as far as the shape distribution is concerned, the axial ratio distribution of BCG_cD galaxies is found to support quite prolate shapes; (iii) our result turns out to be strongly at variance with the only similar previous analysis by Ryden, Lauer & Postman (RLP93), where BCGs and Es were found to share the same axial ratio distribution; (iv) our data suggest that the above discrepancy is mainly caused by the different criteria that RLP93 and ourselves use to select the cluster samples, coupled with a preference of cDs to reside in powerful X-ray-emitting clusters; (v) the GIF2 N-body results suggest that the prolateness of the BCGs (in particular the cDs) could reflect the shape of the associated dark matter haloes.