Follow-up question: How did Napoléon III's Emperorship differ from Napoléon I's if at all?
There was a major crucial difference between Napoleon's office of Emperor of the French and the pre-1789 Bourbon executive: the imperial office existed by virtue of the French Constitution. Although each of the three constitutions progressively increased the power of the executive, the Legislative Body and the Senate still existed under the Empire. Although for most of thier existence Napoleon defanged their constitutional oversight powers and turn them into pliant instruments, they in theory retained the ability to legally depose Napoleon on the grounds that he had violated the Constitution. This salient fact was the linchpin of the Malet conspiracy of 1812 which forged a Senatorial decree that Napoleon was dead in Russia and the Senate had proclaimed a new government. Malet's failure though inspired Talleyrand in the spring of 1814 to get the actual Senate to depose Napoleon. Article 53 of the Constitution of Year XII made Napoleon swear an oath to:
I swear to maintain the integrity of the territory of the Republic, to respect and cause to be respected the laws of the concordat and the liberty of worship, to respect and cause to be respected equality of rights, political and civil liberty, the irrevocability of the sales of the national lands; not to raise any impost, nor to establish any tax except in virtue of the law; to maintain the institution of the Legion of Honor; to govern in the sole view of the interest, the welfare and the glory of the French people.
The Senate's deposing of Napoleon argued that he had violated his oath and therefore was not Emperor of the French, but a tyrant.
This all bespeaks to a wider difference between the pre-1789 Bourbons and the Bonapartes. Although Napoleon found himself ruling a French state far more powerful than hitherto and enjoyed more personal power, he was still bound by the political rules that had been created by the tumultuous events of the French Revolution. Although he tried to circumvent the actual practice of constitutionalism, and largely succeeded in doing so until his military fortunes failed, an important component of his legitimization came from him presenting himself as the exemplar of a modern government, i.e. one with clearly defined legal roles. Napoleon's pre-modern predecessors operated in a much more nebulous world of executive power in which the monarch made pretenses possessing absolute power but often had to govern through delegating authority to various favorites.