What are the differences between Poe's Prospero and Shakespeare's Prospero (from "Masque of the Red Death" and The Tempest)?

There are certainly differences between Poe's Prospero and Shakespeare's Prospero.
First, Poe's Prospero fails to transcend his fate, while Shakespeare's Prospero succeeds in doing so. In "The Masque of the Red Death," Prospero takes on but succumbs to the enemy of his mortality. On the other hand, in The Tempest, Prospero regains his dukedom and is restored to his former privileged life.
Second, Poe's Prospero is ensconced in a position of power throughout "The Masque of the Red Death," while Shakespeare's Prospero spends the majority of The Tempest sequestered on an island, removed from his former sphere of influence.
Third, Shakespeare's Prospero fights his enemies to realize his personal and paternal objectives, while Poe's Prospero is mainly focused on preserving his own legacy.
In "The Masque of the Red Death," Poe's Prospero uses his wealth to protect himself from the plague. With more than a "thousand hale and light-hearted friends from among the knights and dames of his court," Prospero bides his time in one of his sumptuous castles. The castle is surrounded by an imposing wall, and gates of iron prevent the rest of the populace from entering. The plague wields its cruel power over those unfortunate enough to be outside the walls, but Prospero and his friends believe themselves immune from its malevolence.
Inside the castle, they enjoy sumptuous banquets and are entertained by musicians. All remain oblivious to the suffering of the masses. Prospero even holds a masked ball for his guests during their period of confinement. Poe's Prospero believes that his power (which is centered on his position and material wealth) will protect him from the Red Death. Later in the story, he confronts the Red Death himself. However, he is no match for the mysterious villain. Poe's allegorical story highlights the helplessness of the human race: death may be the enemy, but no one can escape it (whether king or pauper).
Unlike Poe's Prospero, Shakespeare's Prospero is not in a position to leverage wealth and power to his advantage. His brother, Antonio, previously conspired with Alonso (the king of Naples) to remove him from his position as the duke of Milan. After his position was usurped, Prospero and his then three-year-old daughter, Miranda, were sent out to sea on an unprotected raft. Their survival was facilitated by the kindness of Gonzalo, a member of the king's council who stocked the raft with food, water, and Prospero's magic books.
In due time, Prospero leverages supernatural means to bring his enemies to his hideout on the island. The only way he can fight his enemies is through magic. Shakespeare's Prospero aims to avenge himself against his mortal enemies for his and Miranda's sake. His goals are not merely selfish. As a father (which Poe's Prospero is not), Shakespeare's Prospero aims to secure his beloved daughter's future. Thus, when he finds Miranda and Ferdinand (the prince of Naples and the son of Alonso) smitten with each other, he is inordinately pleased. In The Tempest, Prospero even tests Ferdinand to ascertain the depth of his love for Miranda.
Later, he insists that Ferdinand will not bed his daughter before the vows are exchanged. It can be argued that Shakespeare's Prospero is a round character (with depth), while Poe's Prospero is more of a flat character. As The Tempest ends, we find Prospero forgiving his enemies. Whether his largesse is inspired by a religious epiphany or Miranda's happiness (or both), Shakespeare does not say. However, it is clear that Prospero has relinquished his bitterness by the conclusion of the play (on the surface, at least).
Having himself obtained the freedom to leave the island, Prospero also releases Caliban (Sycorax's son) from his enslavement. Meanwhile, Poe's Prospero meets a decidedly tragic end, after failing to overcome the spectre of death.