It really wouldn't be that tough. The Han crossbows were simply bows placed on a stock.
http://www.hxlsw.com/UpLoadFiles/Pics/57784601.jpg
The Han xbow's purpose was to be a simple missile weapon that any peasant could use with minimal training. It's a far cry from something like this:
http://cf067b.medialib.glogster.com/...7/crossbow.jpg
...that had some actual piercing power from the technology of its time. Han xbows didn't need to pierce heavy armor so its use against Legionnaires would be of limited value. A line of Roman slingers against Han xbowmen would take heavier initial casualties but then persevere due to higher rate of fire. That is assuming the Legionnaires don't provide cover even.
Truth of the matter is both sides' "xbows" would be inefficient against the other. The Han xbows designed to deal with mostly unarmored tribal cavalry of the north would do little to a Legionnaire and the Roman's manuballistae would not be optimal against lighter armored Han infantry. Bows and slingers would be more capable.
Yeah the Han cavalry would number more but I would say, so what? As for Han army fielding 100,000 professional troops, this simply isn't true. They had a small core standing cavalry army (External/Northern army) which was augmented by limited term servicemen that would serve a couple of years. This is a far cry from the Mariam military system of professional standing troops. As far as logistical capabilities went, Rome had to manage a front on all sides. Han had to deal mostly with the north and a bit of the west. Han history also makes note of numerous times when the northern army got cut off from its resources fighting the tribal armies. Nothing really suggests superior logistics on the part of the Han, if anything quite the opposite.
Oh sure you can compare. The Roman military was designed to fight entities like Carthage, Egypt, Macedon, Persia, while the Han army was designed to counter act northern tribe harassment.
The Han armies got cut off just as much if not more in the northern front as well. There's nothing better about Han logistics.
The Han would field more missile troops but their effectiveness against the Legion would be limited since the Han xbow was not made to pierce such heavy armor but to ward off light/unarmored tribal cavalry.
"However Chinese cavalry commanders would definetely been more knowledgeble of mass cavalry expeditions such as against the Xiongu."
Right, they'd have experience dealing with cavalry based armies, which the Legion was not so irrelevant.
The "professional Han field army" was a small core of imperial guards and officer. The rest were glorified militia.
I wouldn't say they have an advantage as much as I am saying they wouldn't lose as badly to the Romans.