I agree. The comparison should not be made.
I disagree. See post 24 by NextRush, above, in which the argument is made logically and with appropriate references to political parallels, documented from competent eyewitness source material.
Sometimes the analogy is appropriate, and the mistake isn't hyperbole, the mistake is in trying to isolate Hitler as some sort of freak of nature, a once-in-a-millennium Phenomenon the like of which we shall not see again.
Wrongo.
Hitler and his emulators, as documented by William Shirer, are actually the default case for amoral, absolutist, "Nietzschean" leadership freed of historical moral imperatives anchored by absolute values.
I didn't read the Shirer books cited by NextRush, but I did read his Collapse of the Third Republic, in which Shirer surveys 1930's "street politics" in western Europe generally and France in particular, and makes useful comparisons among the various modernist, statist, secular-ideological parties that struggled for power in the aftermath of World War I and the collapse of the traditional European moral and political order. The Communists and Socialists were crushed by the German Nazis in Germany and Austria, but they prospered in France, side-by-side with the native right-wing French Croix de Feu {"Cross of Fire": who does that sound like?). And truth be told, in power the Communists acted like the Nazis, and one is entitled to suspect that any of them, had they been successful, would have acted as the Nazis historically did -- because they all, with the exception of the royalists, operated from similar modernist, statist, "post-moral" premises that would have led them all to similar practices and policies in the end -- just with different policy objects and state victim-lists.
Another way of understanding this point is by reference to an answer that Rabbi Schneerson, long the doyen of the ultra-orthodox rabbis, once gave to the question put to him, "could Jews ever behave like Nazis?" His answer, spat out with distaste for the comparison, was "fruh morgen!": "First thing tomorrow morning!"