There is a hierarchy and a single person at the peak of it who has ultimate executive power (a Chief Executive Officer, if you will) then it'll perform roughly the same as as authoritarian system except in some highly unusual circumstances. A military coup by the army would play out differently for example, but day-to-day operation would be largely the same. And most of the performance differences between democracies and non-democracies come down to democracies having more freedom not to worry as much about generals getting too powerful.

It doesn't matter where the power officially stems from, the decision making bandwidth and incentive structures govern results - and for companies that is a clear authoritarian model.