The Unified Gas-Kinetic Scheme stands out from traditional deterministic numerical approaches to gas dynamics by enabling the resolution of flow regimes ranging from rarefied to continuum, within a simulation time independent of the regime. Its effectiveness in solving complex flows has primarily been demonstrated with Shakhov or Rykov models. Here, we propose to examine in detail the applicability of UGKS to ES-BGK models, extending its application from the monoatomic framework to the polyatomic framework by using recent ES-BGK models that take into account rotational and vibrational energy modes.