It's true that fascism and parliamentary (bourgeois) democracy are two forms of the rule of the capitalist class; and that for socialists, fascism vs "democracy" in the abstract is not the correct way of posing the question.
So therefore we should say "No difference", "We don't care whether fascism crushes bourgeois democracy" etc?! This is madness - like (but worse than) saying "We don't care if there is a monarchy or a republic", "We don't care if women have the right to an abortion" or "We don't care if there are anti-union laws" - since after all, even with a republic, reproductive freedoms and trade union rights, the rule of the capitalists remains. Logically this rules out any struggle for changes or reforms short of overthrowing capitalism and establishing working-class rule.
The point, surely, is that bourgeois democracy, for all its shallowness, hollowness and limitations, is a better form of capitalist rule for the working class to struggle within. Not only because it exercises certain popular limitations on the capitalists' government doing whatever it likes (and because it establishes certain general human rights), but crucially because it allows a certain amount of space for elementary workers' democracy - eg trade unions, workers' political parties - to exist and grow (through a struggle against capital, not by some automatic process). Fascism, by its very nature, destroys all shoots of workers' democracy. That is the role it plays for capital, and why capital helps bring it to power in situations of extreme social crisis.
Clearly that doesn't mean endorsing bourgeois democracy, or giving up on workers' struggle against it. In fact, it flows from the whole analysis that only through independent working-class struggle can we a) win real democracy, ie workers' democracy, and in the short term also expand democratic institutions within capitalism; and b) defeat the growth of the fascist threat. Unity with a section of the capitalists in the name of "democracy" in the abstract undermines both goals.
So in other words we should reject
a) The view that there is "nothing to choose"; but also
b) The view that, because bourgeois democracy is better for the working class than fascism, we should give up our independent struggle against it and for workers' democracy.
Defend bourgeois democracy against fascism - and most crucially, defend the space for workers' democracy to exist and grow - but by the methods of working-class independence and class struggle!