One possible angle is to look at the Latin text, since there is no official adopted Greek text. The article reads:
- Sed Patris et Filii et Spiritus Sancti una est divinitas: æqualis gloria, coæterna majestas.
Though the colon might throw us off, we ought to remember that it did not exist as punctuation in the original, so we might feasibly emphasize the parallelism of this article by reconstructing the passage as follows, followed by my literal translation:
"Patris et Filii et Spiritus Sancti" - "Of the Father and of the Son and of the Holy Spirit"
"est" - is
"una divinitas" - one divinity
"aequalis gloria" - equal glory
"coaeterna majestas" - coeternal majesty
In other words, the Three Persons are said to possess "one divinity" in the same way that they possess the other two qualities. Thus, in this Creed, I would venture to claim that the reference is to the shared glory and majesty of the three persons as one God.
In general, as already mentioned, the "differences" between the Persons are their "ad intra" relations. The "ad extra" actions are of one God.
The larger question--about whether we can refer to a glory particular to the Father or Son or Holy Spirit--is complicated. The most direct Scriptural reference is in the priestly prayer of Jn 17:1-5:
1b Πάτερ, ἐλήλυθεν ἡ ὥρα· δόξασόν σου τὸν υἱόν, ἵνα ὁ υἱὸς δοξάσῃ σέ, 2 καθὼς ἔδωκας αὐτῷ ἐξουσίαν πάσης σαρκός, ἵνα πᾶν ὃ δέδωκας αὐτῷ δώσῃ αὐτοῖς ζωὴν αἰώνιον. 3 αὕτη δέ ἐστιν ἡ αἰώνιος ζωὴ ἵνα γινώσκωσι σὲ τὸν μόνον ἀληθινὸν θεὸν καὶ ὃν ἀπέστειλας Ἰησοῦν Χριστόν. 4 ἐγώ σε ἐδόξασα ἐπὶ τῆς γῆς, τὸ ἔργον τελειώσας ὃ δέδωκάς μοι ἵνα ποιήσω· 5 καὶ νῦν δόξασόν με σύ, πάτερ, παρὰ σεαυτῷ τῇ δόξῃ ᾗ εἶχον πρὸ τοῦ τὸν κόσμον εἶναι παρὰ σοί.
1b Father, the hour has come; glorify your Son so that the Son may glorify you, 2 since you have given him authority over all people, to give eternal life to all whom you have given him. 3 And this is eternal life, that they may know you, the only true God, and Jesus Christ whom you have sent. 4 I glorified you on earth by finishing the work that you gave me to do. 5 So now, Father, glorify me in your own presence with the glory that I had in your presence before the world existed.
In this passage, I would argue that Jesus is speaking of a relational difference in the glory (δόξα) communicated between the Father and the Son. That, however, is a separate question which would merit a separate reply.