I'd have to say that the ground would need to be considered. Where do the empires meet? For example, if Rome advanced through India... well, the mountains of the Hindu Kush are well named. And, given Rome's traditional logistic difficulties and the problems with horse soldiers in southern Asia, Han would have had a definite advantage in mobility and cavalry. The legions were excellently equipped but the scuta has a limited effectiveness.

The question would likely be decided on which empire would use the local resources. I'd actually have to say that the locals would rise up and form empires of their own before either of those two could do anything effective in India - and look what happened.

Perhaps instead the Romans would have been wise enough to set the locals at one another's throats and leave them there as a buffer state... thereby ensuring their own demise once the survivors of generations of internecine conflict banded together against a common oppressor.

As to the Han... presuming equivalent technology is unwise; the Han had basic steel, while Rome had far better roads. Roads trump weapons most of the time, but... let's face it; the distances are simply too vast to permit the conflict. Rome would have split into two separate empires and the Han would have collapsed under internal rebellion long before the two met. (I feel safe in stating this because... well, that's what happened, innit?) Without the steam engine, neither society would have been able to extend that far.

So... my money's on the Han. Of the two cultures, the Eastern Han would have been the most likely to create the steam engine (or an equivalent) and use it for transportation, which would have granted them domination over all of southern and central Asia.