It may seem an impertinence to say so, but Pope Leo the Great seems to think so Catholics are used to the idea that Our Lady is higher than the angels, but is it true for the rest of us? Here is what Pope Leo the Great has to say on the matter. It was surprising to me.

‘The blessed apostles together with all the others had been intimidated by the catastrophe of the cross, and their faith in the resurrection had been uncertain; but now they were so strengthened by the evident truth that when their Lord ascended into heaven, far from feeling any sadness, they were filled with great joy. Indeed that blessed company had a great and inexpressible cause for joy when it saw man’s nature rising above the dignity of the whole heavenly creation, above the ranks of angels, above the exalted status of archangels. Nor would there be any limit to its upward course until humanity was admitted to a seat at the right hand of the eternal Father, to be enthroned at last in the glory of him to whose nature it was wedded in the person of the Son.’ [Excerpt from a sermon by Pope Saint Leo the Great (Sermo 1 de Ascensione, 2-4: PL 54, 305-396) taken from the Office of Readings for Wednesday of the Sixth week of Easter]

If I am understanding this correctly then he is say we can be by grace  at our final end in heaven be raised up as high as it possible to be, seated next to the Son, participating in mystery of the Trinity. The Ascension of the Lord was a sign that man's nature is to divine, although he cannot realise this by his own efforts, hence the need for God's grace. This is an extraordinary privilege.

St. Maximos the Confessor described this as a  “total participation in Jesus Christ.” and said "A sure warrant for looking forward with hope to deification of human nature is provided by the incarnation of God, which makes man god to the same degree as God himself became man.... Let us become the image of the one whole God, bearing nothing earthly in ourselves, so that we may consort with God and become gods, receiving from God our existence as gods. For it is clear that He who became man without sin (cf. Heb. 4:15) will divinize human nature without changing it into the divine nature, and will raise it up for his own sake to the same degree as He lowered himself for man's sake.' (page 178 in the Philokalia, Vol II).

He also said that we will be “All that God is, except for an identity in being, one becomes when one is deified by grace.”

The one question that remains, then for us to think that we can be greater than the angels is this - is the same privilege offered to the angels too? If not, then it seems that we are by nature, greater than the angels (although in are fallen state in this life we are less than them!).