It's important to remember that this is often not an apples-to-apples comparison. Rome and Han expanded at different rates, had different population sizes at different points, and they also had very different systems of military mobilization. Then we also have to factor in potential noise in recorded troop numbers- which numbers are accurate, or inflated, or pure conjecture.

Han and Roman population sizes were comparable around the late 1st century BC/ early 1st century AD, based on census numbers dating to that period (a full national census of Han gives a little over 57 million registered subjects at that time; based off of a partial census of Italy and some guesswork, estimates for Roman population at the same time tend to run between 50-70 million). But in 202 BC, just after the battles of Zama in the Mediterranean and Gaixia in China, Han was already near its maximum size while Rome only ruled a few territories outside Italy. Han reached its maximum extent- pushing to the South China Sea, the Korean peninsula, and the Tarim Basin- around 150 BC while the Roman conquests of Gaul, Pontus and Egypt came a century or more later. This means that, while the "peak" Roman Empire may have had several million more subjects than the "peak" Han Empire, at really any point prior to maybe 50 BC it is likely that Han was more populous.

Han and Rome also had very different militaries and different ways of raising troops. The Western Han system was relatively simple- detailed censuses of all Han territory were conducted regularly, and all healthy adult males were registered for conscription. Every year, a batch of recruits were drafted to train in the standing army and then sent back to their homes, so that most men above a certain age had had at least some formal training. The standing army- which was relatively small, only numbering in the tens of thousands, and was armed by the central government- could be quickly reinforced by hundreds of thousands of conscripts, who owned their own weapons, for a campaign. The system of conscription applied equally to all free men in the Han state.

Meanwhile, Rome had a more complicated system owing to its own city-state roots and its tradition of acting as the head of an alliance rather than as the capital of a unitary empire. Before the Marian Reforms in 107 BC, the Roman army was a citizen militia that provided its own arms, reinforced by "allies" from non-citizen communities. After Marius, the army was made up of professionals who signed long service contracts, lived off their army salaries and were armed and equipped at state expense- but the legionary infantry was still only open to citizens while the supporting auxiliary units were open to "allies." With this the Romans moved away from raising armies ad hoc to deal with situations as they arose, and towards permanent, standing legions kept in constant readiness. This was expensive, but it meant that the Roman state always had strong, professional, well-equipped forces on hand.

(Both Roman and Chinese systems changed significantly over the first several centuries AD, but here I've only covered up to the time of Augustus and the tail end of the Western Han)

Put side-by-side, the Han system had several features that might lend itself to producing larger army sizes even from a similar or smaller population base. One, military service was a universal obligation for people living in Han borders while in pre-Marian Rome it only applied to a certain class (Roman citizens with a minimum amount of property) and post-Marius they only recruited men as needed to fill the ranks of established units (rather than maximizing the total potential number of recruits). Two, the Han system of maintaining only a small standing army during peacetime saved a lot of money- they could afford to mobilize huge forces for short periods of time because they could draw a peace dividend afterwards. Professional Roman forces were more expensive to arm, train and pay, so their size was effectively capped by what the budget could provide for rather than by how much manpower was available.

These two factors, and allowing for some inaccuracy in recorded troop numbers, will likely account for the numbers differences you're seeing.