Hello!
I'm currently watching through the excellent The Great War series on youtube. In this video (hopefully I got the time stamp right) the series claims that Austria-Hungary had a substantially lower amount of available manpower than Russia. While I understand that Russia is much larger, based on this wiki link, Austria-Hungary didn't seem to have such a substantially lower population than their ally in Germany. Yet, they seemed to run into a manpower shortage much earlier.
What gives?
The direct reason was a lack of finances to the army, which stemmed from political problems between the Cisleithanian and Transleithanian halves of the Monarchy.
To elaborate the Austro-Hungarian army had its size limited by a ceiling established in 1889, which was not, despite the increase of the population and significant pressure from the Ministry of War, raised until 1912. The reason for it was that the goverment couldn't allocate necessary funding to support this increase in size. This was caused by a political tension between the two halves of the monarchy; the army expenditure, as well as any army reforms in general, had to be negotiated between them and they were thus basically held hostage to the political/national ambitions and goals of Transleithanian politicians, who used it as sort of a bargaining chip to their own demands of army reforms, with which Cisleithania could not really agree as they further undermined the unity of the state.
Among their demands were for example the desire to have their own Hungarian army, or to at least have the Hungarian language as a language of command alongside German. In the end a compromise of sorts was achieved; the Hungarian Honvéd, the territorial army of Transleithania, was transformed into a basically Hungarian national army that composed of all branches of the army (originally it was limited to only infantry and cavalry, thus excluding artillery) and was not just a second line "home guard" as it was intended; though the primacy of German as a language of command was retained. However this hefty price meant that the manpower ceilings could finally be raised in 1912, though this was still far too late to make that much of a difference, considering that the war would break out less than two years after.
This was by the way also the reason why the Austro-Hungarian army wasn't very well equipped and trained at the start of WWI.
Source:
ROTHENBERG, Gunther E., The Army of Francis Joseph, 1976
Follow up question: does this have anything to do with the fact that outside of congress Poland, Russia had mostly a unified system of conscription, while the Habsburg realms mostly avoided recruiting from the "disloyal" ethnicities like the Slavs and so on?