Compact ellipticals (cEs) are rare objects in the local Universe, but relevant for the evolution of galaxies. Their origin is not completely understood, with evidence equally suggesting that they are relics of early epochs, and remnants of tidal disruptions. This article aims to characterise two cEs, members of the nearby Antlia cluster, providing insights into the formation channels of cEs residing in high-density environments. This dataset consists of archival ACS/HST images and Gemini/GMOS slit spectra. The isophotal analysis of the cEs was compared with their kinematics and stellar population synthesis. The results were also compared with a sample of cEs and `relic' galaxies from the literature, to put them into context. Their characterisations highlight clear differences between the two cEs. Although the stellar populations for both cEs are mainly old, with mass-weighted ages above 10\,Gyr, FS90\,110, the most massive one, has a minor contribution from an intermediate-age population. Besides, it presents rotational evidence, a remarkably bright nucleus for its luminosity, and a clear dichotomy between the inner and outer components. It is probably the remnant of a low-mass disc galaxy that has been tidally disrupted by the close massive elliptical NGC\,3258. On the contrary, FS90\,192 does not present evidence for either rotation or discy isophotes, and its population synthesis leads to a stellar population with ages above 12\,Gyr. It is probably a low-mass analogue to `relic' galaxies.