The edict of Milan didn't formulate Catholicism, it simply made Christianity legal and on equal footing with other religions in the empire. For the development of Catholic theology, that primary stems from the Council of Nicaea and the Council of Chalcedon. The central issue at the Nicaea Council was the question of Jesus's (the son) connection with the Father (God) and if they were on equal footing and essentially one and the same. The counter argument brought forward by Arius of Alexandria that the Son was slightly less than the Father in that the Son had been a created being instead of always existing ( In the beginning was the Word, and the Word was with God, and the Word was God to quote John). What the consul decided was the modern idea of the trinity, that God has three parts (father, son, holy spirit) that are have always existed and are equal to each other and that the Son is begotten of the Father and not made.

The Council of Chalcedon on the other hand, dealt with the issue of Christ's nature and how the human and divine natures of the son manifested themselves. This council was designed to counter the arguments of the Nestorians, who stressed the human nature of Christ and that Mary had not been the Theotokos or 'Bearer of God' ( the aspect of Mary stressed in the Orthodox Church) and the Miaphysites, who stressed Christ's divine nature. What that council agreed on was that Jesus Christ had both a perfect Human nature and Divine Nature that these natures are undivided and unified, and this has remained the standard for Catholics, Protestants ,and Orthodoxy alike.

The other thing I will note is that until 1054, Catholicism and Orthodoxy were essentially one and the same. While the Great Schism had more to do with the issue of power between the Bishop of Rome (the Pope) and the Roman (Byzantine) Emperor, the Schism did include an issue regarding the Trinity in that Catholics postulated that the Holy Spirit comes from the Son and the Father while for the Orthodox the Holy Spirit comes from the Father.

Short Answer, The central tenements of Catholicism came after the Edict of Milan.

Not an expert myself, but I think you'll probably want to help the experts by narrowing down your question a bit more. There wasn't one Christian theology at the time you're specifying. It was Constantine who starting with the Council of Nicaea began the process of unifying and institutionalising a single Christian theology.

Are you trying to ask what the majority Christian opinion was like at the time? Or do you want a breakdown of the major 'denominations'?

Also why did you choose the Edict of Milan and not the Council of Nicea? Are you specifically interested in pre-Nicene Christianity? Or are you more interested in what has changed since Nicea?

I know enough to know early Christianity is a very complicated topic. So I think you'll have better chances of getting the answer you want if you make it a bit clearer what you're looking for.

Church historian and Christian here (of the Lutheran brand). I've got a foot both in the theological and historical issues here which your question poses.

At the time of the Edicit of Milan (313), there was a large amount of diversity of belief among self-professed Christians. From within Christianity, with modern confession lenses, we can define these factions as orthodox or heterodox (heretical). However, historically we cannot answer who is right and wrong on a theological matter, so I'll stay away from using theological definitions other than to indicate whether or not modern Roman Catholicism considers the movement to be orthodox or heterodox.

Here are a summery of the Christian movements present at the time of Constantine's edict.

1. The Gnostics were a larger faith movement that focused on secret knowledge passed from teacher to student as the means of salvation. Christian gnosticism came in a variety of brands, each with their own gospel containing a claim to be the one true path to salvation, through the teaching of a disciple. Hence all the pseudepigraphic gospels. Most gnostic teaching involved a "sharp dualism: they set a transcendent God over against an ignorant creator (often a caricature of the God of the Old Testament)". (Dowley, 68). They are considered heterodox due to this impression of two gods and that creation is evil. The gnostics were most active in the 2nd and 3rd centuries CE. (cf. ibid 68-71).
2. The Arians were another popular group of Christians. They followed Arius who taught that the Son, Jesus, was a created being, not of the same unity with the Father. The old Arian adage "there was a time he [the Son] was not" is the best summery of their teaching. The Arian movement would was very important to our history of Church because it was against this movement that Constantine called the Council of Nicea. They were most active in the 3rd and 4th century. They are considered heterodox due to being in conflict with fundamental Trinitarian theology. (cf. ibid 108-109).
3. The Montanists were a group of people who believed that the Holy Spirit had provided additional revelation through three people (Montanus, Prisca, and Maximilla). They stress a rigorous moral life marked by chastity and fasting and condemned those who did not accept the spirit's teaching. They were condemned very early on as heterodox for their additional teachings and for promoting divisiveness in the early Church. Montanists were most active in the 2nd century. (cf. ibid 73-74)
4. The Monarchians are often known as Modalists because they believed that God existed in different modes - Father, Son, and Holy Spirit - but only one at a time. Traditional Christians answered this with the nuanced but extremely confusing doctrine of the Trinity and condemned them as hetrodox. They were most active in the late 2nd and early 3rd centuries. (cf. ibid 81-82)
5. The Manichaeans were actually just a predominate sect of gnostics but need to be treated separately due to their wider historical context. Like other gnostic teachings, they believed in a duelist nature of created evil and spiritual good. Manachaeism spread throughout the west and lingered through the 4th century. Like all other gnostics, they are considered heterodox by modern Christians. (cf. ibid 91)
6. Apart from the defined heresies above, there were also traditional Christians, as defined by modern Christians, who held the most predominate position among the mosaic through the largest portions of Church history. Their beliefs are more hard to define as they more often define themselves in contrast to the movements above. However, the fundamental aspects of modern Christianity were present: they believed that Jesus was the Son of God, that God existed in Trinity, that Christianity was a continuation of Judaism and that Jesus was one and the same with the god I AM, that the books of the Old Testament were scripture. New books of scripture were also used, namely what is already present in the New Testament today with some local variations. These Christians met weekly on Sunday for worship which included a meal of bread and wine along with scripture readings and sermons. Baptism was the means by which one entered the faith, a process that normally took three years or more if one was an adult. (cf. ibid. 67-100)

When the Edict of Milan was issued, the mainstream Church (no. 6 above) looked similar to modern Roman Catholicism on the largest theological issues but a lot differences can be noted too. Perhaps the best way to understand it is that Roman Catholicism evolved from this early Church; but so did all the magisterial reformers. There are, however, additions. This issue is up for debate, but there was no perspective on the supremacy of the pope. There was no doctrine of transubstantiation or doctrine of concomitance. The sacraments weren't numbered. Other than baptism and communion there wasn't much emphasis on other rites that would later be considered sacraments by the Roman church, like holy orders, extreme unction, confession, and marriage.

While your initial query asks for theological differences, allow me to expand the discussion to two other areas: governance and worship. Naturally the trappings of the papacy did not exist in the 3rd century. There was very little Church order outside of the bishop, priest, deacon structure. Some bishops, known as patriarchs, held higher positions of honor and therefore authority. The bishop of Rome held the highest position, followed by the bishop of Constantinople. Other bishops played important rolls but no one bishop had authority over the other. The Church rather governed through consensus which is why a Church council was called rather than edicts issued from Rome or Constantinople.

As for worship, the mainstream worship forms around Constantine's time and would have looked more Eastern Orthodox but they share a lot of the same elements, form, and prayers of modern Roman Catholicism.

For those interested in Church history broken down quick and easy, I recommend Justo L. González, The Story of Christianity, a two-volume easy read with lots of primary source reading lists for early history.

Works Cited Dowley, Tim. Introduction to The History of Christianity. 2nd edition. Minneapolis: Fortress Press 2013.