As per the stats from Glantz and House's "When Titans Clashed", in World War II, the Red Army generally kept at a strength of just under 7 million soldiers from the mid-point of the war onwards, although far more than that cycled through its ranks during the war, as 11,285,057 died in service during the war.^1

Genghis Khan's forces no doubt varied from time to time, so I haven't found a "never higher than this" peak number, but Stephen Turnbull's "Mongol Warrior 1200-1350" states that his army was only 129,000 at the time of his death, which seems to be based on the writings of Raschid-al-Din. Even when augmented with various auxiliaries it seems to have not been larger than 200,000. Poking through several different books, I'm not seeing any numbers larger than that, so it wouldn't appear the Mongols are anywhere near contention for largest army, whereas several references to numbers much lower than his opponents, such as Weatherford mentioning that in 1207-1209, the Tangut's 150,000 man army was double the size of Genghis', and likewise being seriously outnumbered by the 400,000 fielded by Khwarizm, when his forces plus various allies was in the 150k-200k range.