That's an interesting question! The more obvious question to ask is, "What is the power of the artist in that poem?" In that case, the answer would be that the artist has the power to immortalize the woman in the paintings, forever preserving her youthful beauty and the hopeful dreams of love that she inspires in the artist.
But instead, what is the power of the poet here?
Apparently the poet (or the speaker) has the power to view with objectivity the relationship between the artist and his subject. She can stand aside, outside the minds of the painter and the painted yet still inside the "studio" in which the poem takes place, and she can understand the dynamic between the artist and his subject, then articulate that dynamic. She can point out how the artist has restored all the "loveliness" of the woman, turned her into a "queen" while keeping her a youthful "girl," even elevated her into "a saint, an angel." (We see this power of the poet as an objective observer in other poems by Rossetti as well, such as in "At Home.")
The important aspect of this poet's power reveals itself when the poet (or speaker) starts to see what the artist can't. For the artist, the woman is forever preserved in the paintings as she was at one point in time. But the poet can observe and explain that the woman is now no longer a real source of "hope [shining] bright" for the painter, nor is she any longer a part of the artist's real life but rather a still, silent, and inaccurate image that still "fills his dream."