The Roman Empire had a stronger army than any Greek polis had largely because of the economic power of Rome. Rome was simply bigger and richer than any particular Greek polis and therefore could support a much more powerful military.
The Roman military's power also came from its professionalization and organization. Greek poleis typically had part-time militaries. That is why you could have people like Thucydides serving as officers in the army even though they were not professional. In the Roman Empire, by contrast, the military was highly professionalized. People made their whole careers out of fighting in the military. This was, of course, partly possible because the Roman Empire was prosperous enough and large enough to support a huge standing military.