I think I'm having trouble with this question because you assume that Constantine adopted Christianity at all. I'm taking that to mean that he "converted", though you may be trying to imply something else. But even so, let's go over the tricky idea of Constantine's "conversion."
In the Panegyricus Latinus 6.21 ca. 310 it says:
"For you did I believe, Constantine, see your patron Apollo, and Victory accompanying him, offering you crowns of laurel, each of which represents a foretelling of thirty years. That is, of course, the length of human generations, which are certainly due to take you beyond the old age of Nestorius. And yet, why do I say 'I believe?' You did see him, and you recognized yourself in the image of the one to whom the sacred poems of bards prophesied that the kingdoms of the whole world were due by right. That has now, I think, come to pass, seeing you are, Emperor, like him: young, blessed, our saviour, and a most handsome one. So, quite rightly, you did adorn those most venerable temples with such offerings that they no longer miss their former ones, and now all the temples seem to be calling you to them -- and especially our Apollo, in whose boiling waters are punished perjurers, whom you above all have good cause to hate."
There are also coins from Arles (ca. 313-315) and from London (ca. 317) which show Constantine on one side and the pagan god, Sol Invictus on the other (this would have, of course, been after the Edict of Milan). Not to mention the edicts supporting Haruspicy ca. 321 (CT 16.10.1) and a very interesting bit of graffiti from the Valley of Kings ca. 326, which says:
"I, the torchbearer of the most sacred mysteries of Eleusis, Nicagoras, son of Minucianus, an Athenian, investigated the tombs many lifetimes after the divine Plato from Athens, and I marveled and gave thanks to the gods and to the most devout emperor Constantine who made this possible for me" (IGLT 1265).
Not to mention the blatant continuation of the Imperial Cult found in this inscription ca. 333-335:
"For from our own name we vouchsafe to the community of Hispellum an eternal designation, an appellation to be venerated, so that hereafter the aforesaid city shall be called Flavia Constans ; and in its center we wish, as you desire, the temple of our Flavian Family to be completed of magnificent workmanship, but with this regulation added : that no temple dedicated in our name shall be defiled by the deceptions of any contagious and unreasonable religious belief ; and so we also permit you to stage exhibitions in the aforesaid community, although in such manner that, as has been said, the celebration of Volsinii also shall not fall into disuse through the ages, but that there the aforesaid celebration also must be staged by priests chosen from Tuscia" (ILS, 705).
But let's juxtapose all this information that showed the continuation of paganism alongside the growing Christian concerns of Constantine. Now Eusebius was one of the first and great perpetuators of the idea of Constantine the pious Christian emperor, and he's certainly one of the best known authors of that time. Moreover he met Constantine twice in his lifetime. That being said, there are some very large issues with Eusebius' work, but that doesn't mean we should disregard him completely. We simply need to scrutinise his work with a fistful of salt. So! Let's see what he has to say!
At first Eusebius' account of Constantine's Christianity doesn't seem half bad. In his Historia Ecclesiastica he writes about the victory of Constantine and Licinius under the sign of the Chi-Ro during the Battle of the Milvian Bridge on the 28th of October AD 312:
"Thus when Constantine, whom we have already mentioned as an emperor, born of an emperor, a pious son of a most pious and prudent father, and Licinius, second to him, -two God-beloved emperors, honored alike for their intelligence and their piety,-being stirred up against the two most impious tyrants by God, the absolute Ruler and Saviour of all, engaged in formal war against them, with God as their ally, Maxentius was defeated at Rome by Constantine in a remarkable manner, and the tyrant of the East did not long survive him, but met a most shameful death at the hand of Licinius, who had not yet become insane.
Constantine, who was the superior both in dignity and imperial rank, first took compassion upon those who were oppressed at Rome, and having invoked in prayer the God of heaven, and his Word, and Jesus Christ himself, the Saviour of all, as his aid, advanced with his Whole army, proposing to restore to the Romans their ancestral liberty" (Eus., HE, 9.9.1-2).
He goes on for a bit in this vein. If you want the full account you'll have to go all the way through to 9.9.13, but I won't put all of that here. Later on, though, Eusebius comes back with a far more glorified tale behind Constantine's Christian roots in his Vita Constantini in which he:
Talk about embellishment. Still, this latter account is the one that stuck. Lactantius spoke of the night before the Milvian Bridge as well (Lact., DM., 44), but we can see in later accounts (such as Sozomen, HE, 1.3) that Eusebius' story is the one that everyone followed through with.
Still, Eusebius isn't that cracked up to be. One of his great failures is his complete dismissal and indeed outright excision of Crispus, Constantine's firstborn son from his first marriage, whom Constantine had killed. (One theory is that Crispus slept with Constantine's second wife, and Crispus' step-mother, the Empress Fausta. In fact there's speculation that Fausta was pregnant and she died during an abortion attempt at Constantine's orders. Yikes.) Secular historians, on the other hand, have no qualms discussing the matter of Crispus, as we can see in the Epitomator, Caes., 41.11 and Eutropius, Brev. 10.6 and Zosimus' NH, 2.29. Indeed, Sozomen takes the account of Crispus as a chance to show yet another conversion scene for Constantine as a sign of repentance after Crispus' death (Soz, HE, 1.5) and Julian uses it in a similar fashion, but with pagan gods rather than Christianity (Julian, Caesares, 336).
All of this does not just beg the question "Was Constantine a Christian?" but also, "What did it mean to be a Christian in Late Antiquity?" and "What was the Christian Church like in Late Antiquity?"
These days we have a far more monolithic structure in mind when we think of the Church, but in those days Christianity was just gathering itself up into a reputable station. By the time of the Battle of the Milvian bridge, the Council of Nicaea (325) had yet to occur. The Arian controversy, which would cause uproar within the Church for a good 200 years, had yet to swing around. It was only after Constantine that the Church would finally have enough breathing space to step into the role we more associate with it, though it would have to wait until the 5th century with the Fall of the Western Roman empire to really step into its stride.
Under the Constantinian dynasty, Bishops became a desirous role. Eusebius (though by now, I hope you view him with more suspicion) claims that Bishops acted as imperial advisors to Constantine (VC 1.32). I'll point out that this wasn't the first time Christians had high ranking roles; Lactantius was the rhetor Latinus under Diocletian (he claimed later that Diocletian fired him when he came out as Christian, but I squint at that. Lactantius definitely had an axe to grind. And I mean a BIG axe). But even the Codex Theodosianus gives us reason to believe that Bishops ca. 318 were stepping into more secular roles of power such as judges (CT 1.27.1). Under Emperor Julian, Ammianus Marcellinus, a secular historian, states, somewhat sneeringly, how desirous a role Bishops really had, with their lifestyles sumptuous and their positions in society lauded (Amm. Res., 21.16.18 and 27.3.14-15).
But we can't attribute this all to Constantine. This would have been due to an increasing interest in the East, in Rome becoming increasingly irrelevant, in the senatorial aristocracy losing much of their power, creating a vacuum that Bishops would eventually seize in their stead. It was a process of time. And while Constantine (and Licinius -- let's not forget that Licinius was also involved with the Edict of Milan, though Eusebius would have us believe he was an evil slayer of innocent Christians) opened the gate by allowing Christians to worship in peace and striving to balance the Roman world after the tumultuous 3rd century crisis not long before, Christianity's changes cannot solely be attributed to him.