The difference between saint popes and run of the mill everyday saints may be the larger influence they seem to have. Hilary picked up from where his predecessor left off, confirming the work of several earlier general councils. He continued to rebuild and remodeled many churches desperately in need. He continued to fight Nestorianism and Arianism. But he also accomplished much in his own right, exhorting the faithful and their leaders, and convening several Councils in Rome. We as an institutional Church, benefit millennia later, both from the work he did and the work he continued.
But if that were all, then many of the everyday saints would outshine these popes.
Certainly he did these many historic things. He erected churches, convents, libraries, public baths, and the records of his Roman synod of 465 are the earliest we possess. He continued Leo‘s policy of strengthening ecclesiastical government in the empire. In that he helped define the Church‘s role visa-vi the empire therefore establishing the understanding that the pope, and not the civil leaders (the emperor, at the time), was the leader in spiritual and moral matters.
But it is not all historical. Flowing from those actions he also defended the rights of his bishops to be pastors while at the same time exhorting them to avoid clericalism and be more holy men. He called them to curb the excesses of the time, remember the purpose of their position, and devote themselves more completely to God. He called them to be true shepherds separate from the power of the world. And in a move that may sound familiar, he also completely revamped the ~400 year old Liturgy as a means to modernize church rituals, which were considered too obscure for the new generation of converts and returning schismatics.
And he did all these things in a relatively short reign and this does not even touch his service to Leo before his election.
So he did a great many things we still feel today, but that is not what makes him a saint, but the things he did that increased his holiness and the holiness of others. Those are the things we celebrate today and ask for his intervention in the institution he helped to further and protect.
Jesus spoke to the crowds and to his disciples, saying, “The scribes and the Pharisees have taken their seat on the chair of Moses. Therefore, do and observe all things whatsoever they tell you, but do not follow their example. For they preach but they do not practice. They tie up heavy burdens hard to carry and lay them on people’s shoulders, but they will not lift a finger to move them. All their works are performed to be seen. They widen their phylacteries and lengthen their tassels. They love places of honor at banquets, seats of honor in synagogues, greetings in marketplaces, and the salutation ‘Rabbi.’ As for you, do not be called ‘Rabbi.’ You have but one teacher, and you are all brothers. Call no one on earth your father; you have but one Father in heaven. Do not be called ‘Master’; you have but one master, the Christ. The greatest among you must be your servant. Whoever exalts himself will be humbled; but whoever humbles himself will be exalted.”
-- Matthew 23:1-12