We study the optical evolution of the 2015 outburst in V404 Cyg, with emphasis on the peculiar nebular phase and subsequent decay to quiescence. From the decay time-scale of the Balmer emission associated with the nebula, we measure an outflow mass Mwind ≃ 4 × 10-6 M⊙. Remarkably, this is ˜100 times larger than the accreted mass and ˜10 per cent of the total mass stored in the disc. The wind efficiency must therefore be significantly larger than previous estimates for black hole transients, suggesting that radiation pressure (in addition to other mechanisms such as Compton-heating) plays a key role in V404 Cyg. In addition, we compare the evolution of the 2015 and 1989 outbursts and find not only clear similarities (namely a large luminosity drop ˜10 d after the X-ray trigger, followed by a brief nebular phase) but also remarkable differences in decay time-scales and long-term evolution of the H α profile. In particular, we see evidence for a rapid disc contraction in 2015, consistent with a burst of mass transfer. This could be driven by the response of the companion to hard X-ray illumination, most notably during the last gigantic (super-Eddington) flare on 2015 June 25. We argue that irradiation and consequential disc wind are key factors to understand the different outburst histories in 1989 and 2015. In the latter case, radiation pressure may be responsible for the abrupt end of the outburst through depleting inner parts of the disc, thus quenching accretion and X-ray irradiation. We also present a refined orbital period and updated ephemeris.