So, based on the criteria I laid out before, this is why I'm voting Rome
1) Territorial conquest/political sway: Draw
Rome will win this category over almost every other Ancient Civilization. They conquered more areas than almost any other civilization up until that point (with the possible exceptions of Persia and Han China). And Rome's political influence extended beyond its boundaries. That being said, the Kushan conquered the entirety of its kingdom. First knocking out the Hellenic states in Bactria, then Sythian tribes, and conquering into India and China; both of the latter being very hard to do. So for that, I will give them a huge amount of credit, and call it a draw.
2) Artistic achievements: Draw
I'm going to give the Kushan a bit of leeway here. Both of these cultures' art was heavily influenced by other cultures. For the Romans, it was the Greeks. For Kushan, it was a mixture of Greek, Indian and Chinese. Rome produced a whole lot more, but I won't reward quantity over quality, for now.
3) Scientific achievements: Point Rome
This one definitely has to go to Rome. I went through the whole wiki for Kushan, and it mentioned no scientific achievements of note. Meanwhile we still can't make concrete as strong as the Romans did. Plus the impressive aqueduct systems and other engineering feets the Romans did.
4) Size/longevity: Point Rome
Rome was bigger. Rome lasted longer. It was one of the major powers Kushan was sandwiched inbetween.
5) Lasting impact on the world: Point Rome
A bit arbitrary, but the area Kushan controlled was impacted more by other empires (Mughal, Mongol, etc) than it. Rome had the undeniably greatest impact over the vast areas it controlled. Be it language, religion, architecture, etc. So much of modern Europe is descended from Rome
6) Notable historic figures: Point Rome
There's literally too many to count.
End results 4-0-2 in favor of Rome. So I voted Rome. For what its worth, my vote for Carthage was the result of personal preference after they went 2-2-2.