In this article, we present a numerical investigation of three-dimensional electromagnetic chaotic (Sinai- like) cavities. We computed around 600 eigenmodes for two different geometries: a parallelepipedic cavity with one half-sphere on one wall and a parallelepipedic cavity with one half-sphere and two spherical caps on three adjacent walls. In these cavities we show that the statistical requirements of a well operating reverberation chamber are better satisfied in the more complex geometry due to its spatial and spectral statistical behaviours very close to those predicted by random matrix theory. More specifically, we show that in the range of frequency corresponding to the first few hundred modes, the suppression of non-generic modes can be achieved by reducing drastically the amount of parallel walls. Finally, we compare the influence of losses on the statistical complex response of the field inside a parallelepipedic and a chaotic cavity. We demonstrate that, in a chaotic cavity without any stirring process, the low frequency limit of a well operating reverberation chamber can be significantly reduced under the usual values obtained in mode-stirred reverberation chambers.