Constantine's conversion to Christianity was at best nominal and at no time did he see himself as an "apostle of Christ." Christianity was growing within the Empire, inspite of the persecutions of Diocletian and Marcus Aurelius; and Constantine's conversion was more an acknowledgement of an existing situation than a "monumental step."
Constantine claimed to have seen his famous vision at the Battle of Milvian Bridge and presumably vowed at that time to become a Christian. In fact he had his soldiers place the sign of the cross on their banners. In fact, most of his soldiers were already Christian, so Constantine's actions were something of a concession to his soldiers, not a divinely inspired command. Whatever the truth of his vision, he managed to postpone profession of his own Christianity until he was on his deathbed; and his professed conversion did nothing to stop him from having his own son murdered, whom he considered a rival for power. Since Constantine did not profess his Christianity until his dying moment, he did nothing to inspire others to convert.
As noted above, Christianity was growing rapidly within the Empire. Constantine himself had long worshiped the sun god known as Sol Invictus. His legalization (but NOT endorsement) of Christianity by the Edict of Milan served more to stop persecution (and possibly a rebellion) within the Empire than anything else. The only prominent woman to convert was Constantine's own mother, Helena, who travelled to the Holy Land and claimed to discover the sight of the Holy Sepulcher and the True Cross. Her actions, much more than her son's, promoted the growth of Christianity.
There was no widespread rejection of paganism; the old Roman gods simply faded away, like McArthur's old soldier. The Council of Nicaea, while momentous, was actually called to end quarrels between two factions of Christianity which Constantine feared might devolve into another civil war.
One must not dismiss Constantine's pragmatism. He saw the success of Christianity and knew that it could not be stopped; therefore he legalized it before it became completely unmanageable. His philosophy was more of "if you can't beat 'em, join em." He deserves credit for his pragmatism, but not for anything monumental.
Bottom line, Constantine's conversion made little difference within the Empire other than to stop persecutions. It was not until Theodosius that Christianity was endorsed as the official religion of the Empire.
I can see why the other editor said what he did, but there are a few facts that are important.
1. Constantine did receive baptism at the end of his life. This shows that he was genuine.
2. He chose to be buried in the church of the holy apostle and the created 12 other place where he wanted to put in their relics. What does this say? 13th apostle.
3. If Constantine was a pragmatist, he should not have backed Christianity. It was still small. To follow Diocletian would have been easier. Da Vinci Code is not good history.
4. From a social point of view, the conversion of an emperor makes a huge difference.
This is a very good question. I would say that the conversion of Constantine to Christianity affected the Roman Empire in several ways. This was truly a monumental step in history - whether for good or ill.
First, it gave Christianity legitimacy. In other words, the once persecuted religion now slowly became not only free to worship, but also the freedom to expand with the backing of the emperor. For example, after Constantine, we see new church buildings that would undoubtedly have affected the perception of the people. This, in turn, caused people to become new converts. This affected the empire, because Christianity was monotheistic, which meant a rejection of paganism.
Second, when an emperor converts, it behoves others to follow. In short, there is political pressure and the obtaining of political power to do so. So, more prominent families began to turn to Christianity, especially prominent women. This have made a lasting difference in the Empire.
Third, the church got stronger and this also influenced the Empire. Think of the first church wide council. It took place in 325, the council of Nicaea. It was presided by Constantine, who saw himself as an apostle of Christ. These things encouraged the church to develop and grow more, which shaped the worldview, culture, and mission of the empire, in time.