Their contexts were quite different, and Hobsbawm's "Age of Capital" and "Age of Revolution" are quite apt here. This is setting aside the fact that bearing the same name hardly makes one as capable. I also won't touch on the widespread desire to avoid Napoleonic-scale conflict again (I'm less familiar with this politics - but I'm certain it was a factor).

In the early 1790s, at the early period of the French Revolution, Revolutionary France became tied up in the "Revolutionary Wars". These were characterized by conservative powers invading France, and France invading its neighbors to set up friendly republican governments. These wars demanded dramatic military reform, leading to conscription and the early appearance of modern military organization. Overall it was a cheaper way to run the army, and gave larger armies, and this allowed France to, largely speaking, win the Revolutionary Wars. Further, the post-Jacobin state (far less radical, as the situation was less urgent) needed income, but its weak position between different political factions meant that traditional means of raising income (ie taxes) might destabilize it. The easy solution is to make money through pillaging. Its in this context that Napoleon appears. While he is mythologized, he didn't simply revolutionize military conduct in a vacuum - he utilized the Revolutionary war apparatus of the Jacobins in service of a "pillage" economy (sustain the republic by invading other nations and taxing them). His invasions usually had some other incentive as well (he invaded Russia as he feared it was destabilizing his blockade of Britain).

Napoleon III emerged in a different context - the 1848 revolutions had flared across Europe, a unique moment. Yet they had all been suppressed quickly. The French Revolution of 1848 wasn't a total failure though - it could recover its role as revolutionary leader, but this would require a war mobilization that would necessitate Jacobin politics. Napoleon III was elected largely as a compromise between those-who-would-be Jacobins and Sansculottes, and the liberal bourgeois afraid of Jacobin politics entailed by war mobilization. Thus, as a compromise figure, he was already ill-positioned to harness the military potential Napoleon Bonaparte had been able to tap into (even if he had wanted to). And it was Jacobinism that was feared by the conservative powers, not as much the name "Napoleon", and Napoleon III was more concerned with what might be called a "modernization" or "developmental" program, amidst his powerbroker position in French politics (what might today be called "Bonapartism").

Edit: Altogether, Bonaparte represented a different kind of thing than Napoleon III. Bonaparte was the avatar of an unprecedented social revolution, capable of repeated decisive victory, and setting up radically new political infrastructure (to help facilitate conscription, taxing, etc). He was an inherent threat. He could be nothing else. Napoleon III was not this at all, but someone using Bonaparte`s name to legitimize and strengthen his political power domestically (not to say he didn`t get involved internationally, but this was more standard Great Power interventionism than Revolutionary War). So there wasn`t much point in getting rid of Napoleon III.