However this sort of comparison also yields problems, these problems are that relative prices were very different among countries which makes it difficult to construct exchange rates between currencies (apparently, tanks and planes were relatively cheaper in Germany versus food products like bread, milk, beef and cheese in the Allied countries, a function of the relative scarcity of agricultural land in Germany) and another problem was that prices of military goods like airplanes and tanks changed greatly over time, since during the war these economies learned how to produce these goods.
For example, the average production cost of a Ju-88 was (from Audit reports on Junkers, from http://www.econ.yale.edu/growth_pdf/cdp905.pdf):
1940/41 - 345,536 RM
1941/42 - 307,677 RM
1942/43 - 254,496 RM
And the cost of a comparable medium bomber the B-25 was (from Air Technical Services Command, Budget and Fiscal Office, from http://www.warbirdsandairshows.com/Airc ... tswwii.htm):
1941 - $180,031.00
1942 - $153,396.00
1943 - $151,894.00
1944 - $142,194.00
1945 - $116,752.00
Given the conservative assumption that in 43/44 the production cost of a Ju-88 would decrease to 225,000 RM in 43-44 and 200,000 RM in 44-45 we have that total government expenditures in both countries in terms of tons of empty medium bombers were (fiscal years: September-August Germany, July to June, USA):
---------------- US ------------ Germany
1940/41 ----- 628,351 ------ 2,015,910
1941/42 ----- 1,875,646 ---- 2,858,087
1942/43 ----- 4,557,794 ---- 4,228,033
1943/44 ----- 5,837,821 ---- 5,676,820
*Note in 1940-41 the US was in peace so it's government expenditures were mostly civilian. When it shifted to war, it's volume of expenditures increased much faster than Germany's until 42-43 when Germany's expenditures increased due to the strategic deterioration while US expenditures increased less because they were already "good".
The implicit PPP exchange rate terms here are 2-1.6 RM = 1 which are much lower than those given by "Machine tools and mass production in the armaments boom: Germany and the United States, 1929–44, Ristuccia and Tooze (2013)", who said that military expenditures were compared at 3.8 RM = 1 dollar during wartime. They use that exchange rate on machine tool prices and spend half of the article trying to justify why American machine tools cost more than twice than German machine tools of the same categories (prices were 5,500 dollars and 9,800 RM, in each country) similarly I would find it hard to explain why a medium bomber produced in the US in 43 would cost 600,000 RM while in Germany it would cost 250,000.


Similarly one could compare military outlays between US and the USSR in terms of tanks. In 1943, the USSR spent 125 billion rubles on the war while the production cost of a T-34 was ca. 180,000 rubles, so total 1943 military expenditures were equivalent to ca. 700,000 T-34 tanks. In the US in the 1942-43 fiscal year military outlays were 72 billion dollars and a similarly sized Sherman tank cost ca. 50,000 dollars, so total military expenditures were 1.4 million Sherman tanks about twice of the Soviet level. In Germany a tank like the Panzer Mark 4 was ca. 100,000 marks which means military expenditures in the 42-43 fiscal year were ca. 1.1 million Panzer Mark 4's (the difference between mark-dollar conversion ratio was perhaps larger in terms of tanks than aircraft because the Ju-88 was produced in larger quantities than the B-25 while the Panzer Mark 4 was produced in much smaller quantities than the Sherman and the T-34 so it's cost was relatively higher).
And if we compare military expenditures in terms of soldier pay (how many years of soldier's stipend you can pay), the USSR probably had a large lead over the US or Germany.
These military expenditures estimates were made by converting currencies into dollars using pre-war food prices for US, UK, Germany and Japan, for the USSR I just used Maddison's estimate of the 1940 GDP and USSR's expenditures in comparison to the pre-war GDP figures:

I cross checked the figures for US, UK, Germany and Japan with Maddison's pre-war GDP estimates and found small discrepancies of less than 5% in the case Germany and Japan but a larger discrepancy of ca. 20% in the case of the UK. Still, I think these figures are good enough to get an idea, also notice that in terms of aircraft or machine tools, Germany's expenditures are bigger relative to the Allies than using pre-war food prices.