Easily - they bear comparison. I would certainly understand your objection to comparing them with everything Hitler did. FDR was not Hitler (no mustache) but both of them presided over a period of recovery from economic crises. Their means bear studying.
Each is an example of state intervention to rectify economic depression; in Hitler's case it was a depression following a period of hyperinflation and largescale flight of capital. Hitler's priming of the armaments industries came before FDR was obliged by world events to follow, but both injected government money into a moribund manufacturing industry even outside of armaments, created jobs by doing so, and generated satellite manufacturers. It wasn't, properly speaking, a "Keynesian multiplier" because of the disposable nature of the final product; tanks, once made, generate little further wealth. But it did begin a bubble of expansion.
Where did the actual capital come from? Mostly it was simply printed up by the respective governments, hardly a recipe for permanence, and in fact both countries would have faced economic disaster at some point anyway had not the war placed the principal burden on the losers. Postwar U.S. industrial expansion was brisk in those areas which were either necessary for defense technologies (aeronautics, electronics, etc) or easily convertible to civilian applications (consumer goods such as household appliances and automobiles), or both. That part wasn't sleight-of-hand, it was a real increase in the production of wealth. Its surplus primed the pump for a similar process in Europe.
The point is that (IMHO obviously and subject to debate) while governmental intervention primed the pump it did not cause the economic expansion by itself. The war masked this central fact and in a truly dreadful manner created a market (if you can trivialize razing a city as "creating a market") which allowed the real expansion growing room. I suggest that it also masked the inadequacy of government to do anything but prime the pump and encouraged people that government intervention was responsible for more than it really was. There, I think, is the real playing field for debate between liberal and conservative economic policy proponents.
Let me elaborate a little bit on the mindset of the interwar years - which was truly quite different than that of today. Keynesianism looked much better than it does now and people were very, very worried about the future of the American dream. Look at how many sided with Hitler or Stalin. In this context let me ask you to elaborate on your statement
and in fact both countries would have faced economic disaster at some point anyway
and what you would have done had you been in Hoover's or FDR's shoes.
...and in a truly dreadful manner created a market (if you can trivialize razing a city as "creating a market")...
It may be truly dreadful but far too often this is the manner in which markets are created. See my earlier post about the Black Death.
To return to today. Nobody deals well with economic contraction, failure, eviction, starvation, etc. Priming the pump obviously has a down side. Safety nets are a function of prosperity. They disappear when the going gets really tough. The contention that downsides will be short and sharp sans government intervention seems to me about as reliable as the contention that war will be short and victorious. I am not persuaded that anyone - anyone at all - has a real grasp on what makes the economy tick.