The X-ray transient IGR J18245-2452 in the globular cluster M28 contains the first neutron star (NS) seen to switch between rotation-powered and accretion-powered pulsations. We analyse its 2013 March-April 25 d long outburst as observed by Swift, which had a peak bolometric luminosity of ˜6 per cent of the Eddington limit (LEdd), and give detailed properties of the thermonuclear burst observed on 2013 April 7. We also present a detailed analysis of new and archival Chandra data, which we use to study quiescent emission from IGR J18245-2452 between 2002 and 2013. Together, these observations cover almost five orders of magnitude in X-ray luminosity (LX, 0.5-10 keV). The Swift spectrum softens during the outburst decay (photon index Γ from 1.3 above LX/LEdd = 10-2 to ˜2.5 at LX/LEdd = 10-4), similar to other NS and black hole transients. At even lower luminosities, LX/LEdd = [10-4-10-6], deep Chandra observations reveal hard (Γ = 1-1.5), purely non-thermal and highly variable X-ray emission in quiescence. We therefore find evidence for a spectral transition at LX/LEdd ˜ 10-4, where the X-ray spectral softening observed during the outburst decline turns into hardening as the source goes to quiescence. Furthermore, we find a striking variability pattern in the 2008 Chandra light curves: rapid switches between a high-luminosity `active' state (LX ≃ 3.9 × 1033 erg s-1) and a low-luminosity `passive' state (LX ≃ 5.6 × 1032 erg s-1), with no detectable spectral change. We put our results in the context of low-luminosity accretion flows around compact objects and X-ray emission from millisecond radio pulsars. Finally, we discuss possible origins for the observed mode switches in quiescence, and explore a scenario where they are caused by fast transitions between the magnetospheric accretion and pulsar wind shock emission regimes.