To be perfectly honest, this analogy makes no sense.

There is a tradition in various Marxian circles to see "Bonapartism" (also called Caesarism too) as one of the alternative politics of the bourgeois political order in which a military strongman seizes power on promises of order. A number of Trotskyites and other left-wing opponents of Stalin did assert that the Soviet leader was acting in a Bonapartist manner. This charge itself does not carry much weight in contemporary Soviet studies; Stalin's dictatorship operated far differently than the models of a military dictatorship.

But applying the Stalinist moniker to Napoleon I is even more fraught. Napoleon built a strong French state and was a harbinger of centralization, but the First Empire was anything but totalitarian. Fouche's secret police was not an instrument of mass repression and did not particularly stand out compared to its contemporaries' in terms of censorship or other police repression. The differences between Napoleonic France and the Stalinist USSR are quite stark.

The liberal charge for Napoleon is a bit more difficult. The French Revolution was the beginning of French classical liberalism's political life. A number of revolutionaries did champion constitution, an end to state monopolies, an end to censorship, and other Enlightenment-era precepts of good government. Benjamin Constant in particular emerged as the champion of French liberal thought and emerged through the Revolution intact.

Napoleon's relationship with the liberal wing of the Revolution was quite complex. On one hand, he did champion greater rationalization of the state and did create a constitution. However, Napoleon preferred his constitution to be "short and vague" and really had little preferences to smaller states and free markets. He instituted a degree of trade protectionism and reimposed state monopolies as a form of state revenue. The relationship between Napoleon and French liberals was quite tense. Constant became a political persona non grata after 1803 and only reemerged in French politics during the Hundred Days. This brief period, termed by some Napoleonic historians the "Liberal Empire" because Napoleon treated with French liberals to shore up his domestic support after his escape from Elba.

But the liberal empire moniker was just that, a moniker. Napoleon's relationship with French liberals remained quite tense during the Hundred Days and there were signs this political alliance was fraying before Waterloo. Napoleon's engagement with French liberal ideas had often been an amalgamation of tactical maneuvers and the practical. Having a vague constitution denied liberals a political grievance, but also won over those elements of the French political classes tired of revolutionary politics and suited Napoleon's penchant for ordered solutions to political problems. Napoleon may have used liberal ideas, but it was in service of Napoleon's own conceptions of the state. This was an exercise of power that was very different than Stalin's dictatorship.

So the analogy is not a particularly good one and does not have much evidence to support it.