Alexander's was bigger I believe, certainly it was bigger culturally, with the Greek peoples (minus the Spartans and the Greeks in Italy) who had always famously eluded the Persians. It also spread into places like Bactria and India, which was further than the Persian Empire under Cyrus would expand. Egypt also was not added under Cyrus, but under Cambyses II, so that would be another point in Alexander's favour.

But there is also the idea of time to factor in, yes Alexander has a disproportionately large empire, but Cyrus founded one of the ancient worlds great super powers, the Persian Empire. Alexander's legacy was more about him as a person and as a general, than as the founder of an Empire.