The instruments developed for the upcoming Extremely Large Telescopes (ELTs) will need efficient adaptive optics (AO) systems to correct the effects of the atmospheric turbulence and allow imaging at the highest angular resolution. One of the most important requirements for ELT AO-assisted instruments will be to deliver diffraction-limited images in a significant part of the sky. For that, the instruments will be equipped with laser guide stars (LGSs) providing most of the information required by AO instruments. But even with LGSs, AO systems still require the use of natural guide stars (NGSs) to compensate for image motion (jitter) and some low order aberrations. These NGSs are eventually limiting the fraction of the sky that can be achieved by AO systems, the so-called sky coverage (SC). We first present the SC assessment methods used for high angular resolution monolithic optical and near-infrared integral field spectrograph (HARMONI) and multiconjugate adaptive optics relay/multi-AO imaging camera for deep observations (MAORY/MICADO), that are both instruments for the ELT of the European Southern Observatory (ESO). They are based on a semianalytical description of the main contributors in the AO error budget, allowing for a fast estimation of the residual jitter. As such, these methods are well suited for statistical estimation of the SC on multiple science fields and/or to efficiently explore the system parameter space. We then compute the SC of the two instruments in cosmological fields from the cosmic assembly near-IR deep extragalactic legacy survey catalog. The goal is to provide an insight on the possibilities given by two different types of tomographic AO systems, i.e., laser tomography AO with HARMONI and multiconjugate AO with MAORY, on the same telescope. In particular, we show that HARMONI and MAORY/MICADO are complementary, meaning that the overall SC of ESO’s ELT is much improved for applications common to both systems.