Depends on what kind of socialism you’re talking about. Under authoritarian socialism—which is very often the one referred to in the mass-media, the USSR kind—very little would change. The state would control corporate surplus and the superrich would simply change their ideological costume—which they’re very good at doing. A better term for this kind of socialism is ‘state capitalism’.

The kind of socialism that Bernie Sanders and Jeremy Corbyn promote is a benign version of this. As it stands at the moment the state is the best defence we have against corporate totalitarianism (not a term I use lightly; corporate structures are perfectly totalitarian—top down and requiring unquestioning obedience) and Sanders-Corbyn (also Podemos in Spain and, to some degree Syriza in Greece) understand this very well. They want to use the state to create a benign form of capitalism; to heavily tax corporations and the super-rich, to make them more accountable, to punish them for capital flight and environmental crimes and so on. This, combined with things like citizen’s income, land reform, electoral reform, public works programmes, debt-reduction, dismantling or reduction of the military-corp-funding-system (none of which have actually been proposed by these groups, as far as I know, but which are perfectly consonant with their approaches) would create a fairer and more egalitarian market-system. The ideal, more or less, is something like that of the mid 20th century political reformers, the kind that gave the UK the NHS and that gave the US the new deal. I suppose the best term for this is ‘democratic socialism’ or ‘reformist socialism’ or something like that.

In full-blown libertarian socialism, the kind that I support, which is probably better described as anarchism, workers do not just have a say in how their worklives are run, they don’t even just own the ‘means of production’, but they, critically, control surplus. Workers can decide what they do with their output and their profits. This is pretty much the diametric opposite of what we have now—there wouldn’t be what we understand as corporations under this system, but fluid anarcho-syndacalist societies that are based on mutual aid. Personally, I also believe this is flawed, because it is excessively rational and doesn’t take into account that in reality that is the sine qua non of any functioning human unit, but of current political ‘isms’ it is the best.