Analytical and numerical results from recently developed strongly nonlinear asymptotic models are compared and validated with experimental observations of internal gravity waves and results from the numerical integrations of Euler equations for solitary waves at the interface of two-fluid systems. The focus of this investigation is on regimes where large amplitudes are attained, where the classical weakly nonlinear theories prove inadequate. Two asymptotically different regimes are examined in detail: shallow fluids, in which the typical wavelengths of the interface displacement are long with respect to the depths of both fluids, and deep fluids, where the wavelengths are comparable to, or less than, the depth of one of the two fluids. With the aim of illustrating the breakdown of the asymptotic assumptions, the transition from a shallow to a deep regime is examined through numerical computation of Euler system's solutions and by comparisons with solution to models.