A: Roman auxillarys:
Roman auxiallarys where no cannon fodder, in fact, troops like the Sarmatian cavalry or Germanic heavy infantry fought a bit differently but not worse than the Romans.
In addition, the thing with the roman auxiallarys was that they could became romans if they fought well.
Former "auxillarys" like Arminius became, although born Germans/Gauls/Sarmatians, "knights" of the Roman empire.
The fact that the roman legions werent conscripts was one of their main advantadges.
They were often worse equipped as the Legionaries. There's a reason why the Auxilia infantrymen wore lorica hamata instead of the lorica segmentata.
B: Height
In addition, after my own experience in China, i think that the height difference may also be a factor.
As far as I know, the average roman was bigger than the average Chinese, while a Germanic/Gaulish auxiallary was significantly bigger.
Its not so much of a factor in actual combat, but its quite effective in a psychologic way.
That is a common myth. Chinese were actually very tall peoples in ancient times, read PiSigma's post. Chinese are actually recovering their height very rapidly nowadays due to improved nutrition.
C: Running away:
I have read the 3 Kingdoms, as well as similiar works like the Gallic Wars or Germania by Caesar or Tacitus.
The theme of the commanding officer beeing killed or even only forced of in a preliminary duel, followed by a rout of his army, was extremly more frequent in the three Kingdoms.
Prelimanry duels did not happen in Rome (They sometimes happened in fights between Barbarian tribes, but also rarely. In addition they ended with one guy getting killed instead of one guying beeing forced back). Also, Romans did not flee that much when their general was killed.
You've read SanGuoYanYi, or Romance of the Three Kingdoms, not SanGuoZhi, or Three Kingdoms ambition (may be mistranslation here). SanGuoZhi is the history, SanGuoYanYi has a lot of fictional parts. In actual history Chinese generals DID NOT duel the enemy's general, and the Chinese troops, of course, DID NOT retreat.
D: Tactically:
The Chinese could counter the superior Roman infantry by using their sophisticated shooting tactics, the Romans could counter by attacking at night or doing other things to disrupt the chinese order.
Both armys had the neccesary means of dealing with the enemy, it would come down to the individual commander.
See PiSigma's account.
Realize that Chinese troops did not only employ great tactics, they often used other ways to weaken the enemy before even engaging them, such as using attrition and morale as a weapon, etc. You claimed to have read the Three Kingdoms yet you know not of these strategems that were frequently employed.
E: Logistics:
However, a real war between these nation would have ended in a draw.
There is no way to supply forces big enough to be a threat in such a distance from your own base of power.
Can you imagine the logistic nightmare of having to ferry 100.000s of chinese troops from the Yangtze to Byzantium?
Or getting Heavy Germanic/Gaulic auxilia through Persia without pissing off the entire population?
There could have some limited border clashes, a Legion getting shot to pieces, a chinese detachmen getting ambushed but not much more.
Even back in the Qin Dynasty (Which was the dynasty before Han), China (to be more specific, QinShiHuang) has built great highways for chariots and troops to travel on, and these highways were no less efficient than the Roman road systems. Qin was an authoritarian dictatorship, and they needed these highways to suppress the people.
See IDont's post.
Last Centurys Chinese beeing taller than Europeans? Pretty unlikely, as reports from last centurys western diplomats in China claim them as beeing petty small.
I would like to see a link of that. You're probably thinking of Koreans or Japanese, because they, unlike Chinese, were indeed very short peoples in the old days.
Actually, Chinese 1on1 fighting systems like WuShu also claim that, assuming roughly equal skill, the bigger guy will win.
This is open war, there will not be any 1v1.
I highly duobt there are any WuShu books or master that would say "The bigger guy would win in this circumstance." I would stand corrected if you can prove it to me.
In a fight, height is a positive factor, and can get pretty important in a mellee.
The point is moot. I think we can all agree that Chinese were just as, if not higher, than Romans and Gauls.
Yes, they where within one day from each other, however, they could not expand much more because they just reached the end of their possible expansion.
Now THAT is a desperate argument.
The size of the army one can succesfully keep in the field dircetly depends on the distance from the own base of power.
Assuming that you've read Three Kingdoms, you know that Chinese troops have more ways to get food than shipping them from China.