The Nazis have been entertainment's go-to bad guys since 1941 (wonder why). Indiana Jones does his best archeology work when he's punching Nazis in the face, and William "BJ" Blazkowicz has probably killed more Nazis during his tenure as the hero of the Wolfenstein video game series than there were actual Nazis in history.
But Guido isn't exactly a face-punching, gun-toting, testosterone-laced hero of yore, so Life Is Beautiful takes a different approach to Nazis. They're still the antagonists, but things are a little less Saturday-morning cartoon villain here.
So how does the film use the imagery of the Nazis symbolically? First, let's briefly break down what Nazism, more specifically National Socialism, believed.
National Socialism was an extreme form of fascism, a political ideology that promotes "militaristic nationalism, contempt for electoral democracy and political and cultural liberalism, a belief in natural social hierarchy and the rule of elites, and the desire to create a Volksgemeinschaft (German: 'people's community'), in which individual interests would be subordinated to the good of the nation" (source).
In short, whatever makes your nation stronger is good, and the needs of individuals and other nations mean nothing. It helps if you can find enemies, many enemies, to coalesce your nationalism around. And if you can pin all the nation's troubles on those enemies—Jews, say—then the solution is final and simple: eliminate them once and for all.
If you subscribed to the National Socialist ideology, you turned your individuality over to that ideology and your totalitarian leader—all of you, body and mind. Life Is Beautiful instills this fact into its Nazi characters.
Note that, with the exception of Dr. Lessing, none of the Nazi characters have names. They also lack distinguishing personalities. They're all two-dimensional, stern, humorless, and unnaturally stiff-backed. They have no relationships with other people. They also yell—like, a lot.
Now compare the Nazi characters to most of the other characters. Characters who don't subscribe to Nazism have a variety of personalities, from the fun-loving Guido to the self-absorbed Rodolfo to the street-smart Bartolomeo. They have relationships and lives beyond their social roles. They even have names and can speak in tones other than "angry headmaster."
These contrasting characteristics clue us in to the film's argument against National Socialism. This worldview not only leads to atrocities like the Holocaust, but it also strips those who follow it of their individuality. They're no longer people in the eyes of their nation; they're just cogs in the machine.
And while it is certainly fun to watch Hellboy beat up Mecha Hitler, we've gotta say that Life Is Beautiful's more nuanced approach to Nazi villainy will stick with us a bit longer.