According to Eusebius Ecclesiastical History, what was it about Christianity that attracted Constantine?

Eusebius Pamphilus of Caesarea (d. 339 C.E.) begins his Ecclesiastical History by noting that Constantine was essentially honored by God from the very start of his life, so though he was not born a Christian, he was always predisposed to Christianity and displayed piety, virtue, and godliness even before his conversion. Eusebius compares him to Moses, painting him in a prophetic light and writing in Chapter XII (12) that he was

brought up in the very palaces and bosoms of the oppressors, and instructed in all the wisdom they possessed. And when in the course of time he had arrived at manhood, and the time was come for Divine justice to avenge the wrongs of the afflicted people, then the prophet of God, in obedience to the will of a more powerful Lord, forsook the royal household, and, estranging himself in word and deed from the tyrants by whom he had been brought up, openly acknowledging his true brethren and kinsfolk. . . . And in the midst of these, Constantine, who was shortly to become their destroyer, but at that time of tender age, and blooming with the down of early youth, dwelt, as that other servant of God had done, in the very home of the tyrants, but young as he was did not share the manner of life of the ungodly: for from that early period his noble nature, under the leading of the Divine Spirit, inclined him to piety and a life acceptable to God. A desire, moreover, to emulate the example of his father had its influence in stimulating the son to a virtuous course of conduct

In other words, despite the fact that Constantine was an elite Roman and was not born a Christian, he always behaved like a Christian, and he was always intended to destroy the Roman tyrants who oppressed Christians. You should also note that Eusebius mentions Constantine’s father. He hints that it was indeed his illustrious father and his own good treatment of Christians and good behavior that attracted Constantine to the faith. In other words, his father served as a model. This is why Eusebius devotes quite a few chapters to him as well.
Ultimately, around 312 C.E., Constantine seems to have experienced religious visions which motivated him to convert to Christianity. Eusebius addresses these episodes in chapters XXVII–XXXII (27–32). While praying for a good outcome in an upcoming battle, Eusebius notes that the shape of a cross appeared to Constantine. Later, in a dream, he was visited by Christ, who commanded him to mark his armies with the sign of the cross in order to protect and guarantee them victory. This is considered his official religious epiphany and conversion to Christianity. He was the first Roman emperor to do so.
https://sourcebooks.fordham.edu/basis/vita-constantine.asp