I think the argument is that democracies tend to be more stable. Weimar was an attempt to patch together a democratic successor to a fairly authoritarian state, and Louis XIV's rule was at best metastable. Near the end of his reign, the War of the Spanish Succession (among other things) was causing France to begin to run into the financial difficulties that would cause Louis XVI trouble.

More generally, if Amartya Sen is right (http://en.wikipedia.org/wiki/Amartya_Sen#Research), democracies are rather less likely to do things that would lead to popular unrest.