In many accounts of this period we hear of armies numbering in the hundreds of thounsands and sometime as high as 500 000 on both sides for a single battle.
There are a couple of considerations on these issues:
1) Duration of battles. The standard Warring States battle involves cautious maneuvering, fort-construction, and a lengthy observation period before battle is definitively engaged - all of which drags out the length of these battles (the entire Changping campaign stretches on for 2,3 years). In that period soldiers will rotate in and out of the active 'battle', and so the number of 'participants' will evidently be inflated because of this.
2) The majority of Warring States during this period had a very high level of control over their populations which no European country could ever match (on a country-wide basis, at least). Resettlement/relocation of villages to garrison the frontiers was a fairly common occurrence, and conscription of soldiers was the order of the day. So a major limiting factor for European armies - actually having the bureaucracy to raise such an army - did not exist to such a degree in China.
3) The administrative structures of the proceeding Han Dynasty certainly indicate a high level of control by the central government over the lives of ordinary people. The Han government was not only able to keep tabs on who was to be conscripted in every given year, it was also sophisticated enough to be able to process offers for those who wanted to buy their way out of conscription (for example, by offering up a good horse or paying somebody else to serve in their place).
We also get the scale of typical mid-Han armies in the Xiongnu campaigns of Emperor Wu, which record around 200,000 men in total spread across 2 or 3 coordinated 'prongs'. The numbers involved in Warring States battles would probably exceed that, since inter-state competition was so much more fierce.
At the same time in the west, during the hellenistic and roman era, it seems that armies rarely reached the 50 000 mark and were always smaller than 100 000 men. Apparently there were extremely compelling logisitcal reasons for that. A marching army of 100 000 people was simply impossible to feed given the tools of the time.
The logistics for massive Chinese armies is lightened somewhat by the fact that most of the grain used to sustain a Chinese army of that size would probably have been transported along the rivers and canals of China. The Qin Dynasty, for example, built the Ling Canal, which connected the Yangtze River Delta with the Pearl River Delta, precisely to facilitate this type of military movement.
Beyond the range of reliable river transport, Chinese armies were subject to the same logistics concerns as those in Europe, as can be seen in the various difficulties encountered with even small armies in fortress sieges in the mountains of Shanxi. The Chinese riverine system is a fair ways more interconnected than the European one (at least from a Roman Empire viewpoint), however.
What does that mean ? Are the chinese figures (vastly) exaggerated ? Or was rice easier to transport than wheat ? Or what ?
One additional problem that can skew the figures of Chinese militaries is that generals frequently do not report allied casualties and instead exaggerate enemy deaths. That said, the assertion of some scholars that Chinese army estimates have to be reduced by a factor of 10 is probably too much, and an army count of a few hundred thousand (over time) near navigable rivers would not be entirely unbelievable, especially if the stakes were high enough.