Objection 1. It would seem that the angels will judge. For it is written (Matthew 25:31): "When the Son of man shall come in His majesty, and all the angels with Him." Now He is speaking of His coming to judgment. Therefore it would seem that also the angels will judge.
Objection 2. Further, the orders of the angels take their names from the offices which they fulfill. Now one of the angelic orders is that of the Thrones, which would seem to pertain to the judicial power, since a throne is the "judicial bench, a royal seat, a professor's chair" [Cf. St. Isidore, Etym. vii, 5. Therefore some of the angels will judge.
Objection 3. Further, equality with the angels is promised the saints after this life (Matthew 22:30). If then men will have this power of judging, much more will the angels have it.
On the contrary, It is written (John 5:27): "He hath given Him power to judgment, because He is the Son of man." But the angels have not the human nature in common with Him. Neither therefore do they share with Him in the judicial power.
Further, the same person is not judge and judge's minister. Now in this judgment the angels will act as ministers of the Judge and, according to Matthew 13:41: "The Son of man shall send His angels and they shall gather out of His kingdom all scandals." Therefore the angels will not judge.
I answer that, The judge's assessors must be conformed to the judge. Now judgment is ascribed to the Son of man because He will appear to all, both good and wicked, in His human nature, although the whole Trinity will judge by authority. Consequently it behooves also the Judge's assessors to have the human nature, so as to be visible to all, both good and wicked. Hence it is not fitting for the angels to judge, although in a certain sense we may say that the angels will judge, namely by approving the sentence [Cf. 1].
Reply to Objection 1. As a gloss on this passage observes, the angels will come with Christ, not to judge, but "as witnesses of men's deeds because it was under their guardianship that men did well or ill."
Reply to Objection 2. The name of Thrones is given to angels in reference to the judgment which God is ever pronouncing, by governing all things with supreme justice: of which judgment angels are in a way the executors and promulgators. On the other hand, the judgment of men by the man Christ will require human assessors.
Reply to Objection 3. Equality with angels is promised to men as regards the essential reward. But nothing hinders an accidental reward from being bestowed on men to the exclusion of the angels, as in the case of the virgins' and martyrs' crowns: and the same may be said of the judicial power.
Source: Summa Theologica (New Advent)