The phenomenon of active turbulence, a complex organization of matter driven at the scale of its constituent agents, is puzzling. Specifically, the lack of scale-separation in low-Reynolds-number active flows breaks away from the familiar notions of the energy cascade and approximate scale-invariance of inertial turbulence. Here, using a generalized hydrodynamic model developed for bacterial turbulence, we provide compelling analytical and numerical evidence that, beyond a critical drive, active turbulence indeed attains universality akin to inertial turbulence. In this asymptotic state, the energy spectrum scales as k−3/2, reminiscent of some classes of inertial turbulence. The flow also exhibits spatio-temporal intermittency beyond the transition, as seen from non-Gaussian fluctuations in velocity differences. With these tell-tale fingerprints, active turbulence is placed closer in phenomenology to inertial turbulence than previously held. We show, however, that as a consequence of a finite range of scales, the degree of chaoticity and hence mixing efficiency saturates to a maximum in the asymptotic regime, unlike unbounded chaos in inertial turbulence. We conclude that active turbulence, depending on the level of drive, can switch between fundamentally distinct non-universal and universal states. Active fluids exhibit regimes with a complex spatio-temporal structure reminiscent of inertial turbulence. Now, inertial and active turbulence are theoretically shown to be closely related indeed.