How do Alonso and Antonio in Act 2 of The Tempest compare to Prospero's enemies in Act 1, scene 2?

In Act I, Scene II, Prospero is speaking to Miranda and telling her how they came to be on the island. He describes his brother Antonio’s treachery. Prospero enjoyed studying and concentrated on that more than on governing Milan. He left the governing of Milan to Antonio, his brother. Antonio immediately began scheming with Naples to take the Dukedom from his brother. “My brother and thy uncle, called Antonio—I pray, mark me!—that a brother should be so perfidious!” Eventually, Antonio moves in, and with help from an army sent by Naples, he takes the Dukedom and sends Prospero and Miranda off to die on the ocean. "This King of Naples, being an enemy to me inveterate, hearkens my brother’s suit…a treacherous army levied one midnight…"

In Act II, we meet Antonio and Sebastian, the brother of the King of Naples. Antonio, who has stolen his brother’s dukedom, is now encouraging Sebastian to seize his brother’s throne by murdering him. Sebastian is a little reluctant, at first, but then he remembers that Antonio took his brother’s dukedom: “I remember you did supplant your brother Prospero.” After Antonio reassures him that he will be glad when his brother is dead, he encourages Antonio to kill the king, telling him he will no longer owe taxes to Naples. “Draw thy sword. One stroke shall free thee from the tribute which thou payest.”

The comparison is simple. In the first act, Prospero is talking about the treachery of his brother and his enemy. In the second act, two of the people who conspired against him are contemplating the most treacherous act of all: killing a king.

In Act 2, Scene 1 of The Tempest, how does Shakespeare portray Sebastian and Alonso as antagonists?

The very opening of Act II scene 1 indicates the conflict between Alonso and his brother, Sebastian. Note the context. As the scene opens, Alonso is clearly struck massively by grief because he fears his son, Ferdinand, has died in the shipwreck. Gonzalo, the faithful retainer, tries to comfort his lord, but Sebastian only mocks his brother cruelly, given the situation. Consider what he says to Antonio as he listens to Gonzalo's words of comfort:

He receives comfort like cold porridge.

Such childish attempts to make fun of his brother and of Gonzalo show Sebastian to be a petty, vindictive individual who, as the scene develops, is shown to be actively opposed to his brother. He is very easily tempted into trying to kill Alonso by Antonio, even when Alonso seems to do nothing to warrant an emnity between himself and Sebastian. Even when Sebastian apparently tries to comfort Alonso, he ironicaly offers comfort that can only be described as "cold porridge," when he tries to say that Alonso should be glad for his loss as it means his daugher is far away from him and won't be able to sadden him with her presence. Hardly sympathetic words.

Assess the characters of Antonio and Sebastian in The Tempest.

Antonio and Sebastian are two of the ship’s passengers who wash ashore on the island where Prospero, the magician, and his daughter, Miranda, live. Antonio is Prospero’s brother; he became the Duke of Milan by usurping the position from Prospero, who is determined to recover control of the territory. Sebastian is the younger brother of Alonso, the king of Sicily. Sebastian is presented as a parallel character to Antonio, who goads him to take over Sicily by murdering Alonso and his adviser Gonzalo; they are thwarted by magic. Both characters help Shakespeare emphasize the difference between legitimate and illegitimate accession to a political position.

Although Antonio is more evil, Sebastian is both greedy and cruel. When they are washed ashore, Alonso believes that his son and heir, Ferdinand, has perished at sea. Rather than offering encouragement that he may have survived or sympathy for his apparent loss, Sebastian blames Alonso because the reason for their voyage was to attend his daughter’s wedding, of which Sebastian disapproves.

Later, when Ariel and Prospero wreak enchantments on the shipwrecked men, they miss Antonio and Sebastian, who thus remain awake as the others sleep. Their villainy is established through their decision to kill Alonso and Gonzalo as they sleep. Antonio’s motive is to gain an ally who will free him from the tribute that he currently pays to Alonso. In his persuasive speeches to Sebastian, Antonio rationalizes that the takeover is their destiny (act 2, scene 1):

by that destiny to perform an act
Whereof what's past is prologue, what to come
In yours and my discharge.

When they draw their swords, however, another one of Ariel’s magic spells wakes up the sleeping men. The would-be assassins pretend to be loyal guardians. Intervening in their actions was not simply an ethical issue, however. The plot against Alonso was not in Prospero’s interest, because he wants Ferdinand, Alonso’s son, to marry Miranda, thereby uniting the two territories.

In The Tempest, are Antonio and Sebastian's criticisms of Gonzalo justified? What does this reveal about their character?

In act 2, scene 1, Antonio and Sebastian do more than criticize Gonzalo; they are actively mocking him. This scene takes place after the shipwreck, when these characters have washed up on Prospero's island, and morale (naturally) is at a low. Gonzalo is seen here speaking optimistically about their situation, stating that they should count themselves fortunate that they survived the shipwreck at all. All the while, Antonio and Sebastian are seen constantly belittling his words.

When discussing Gonzalo, Antonio, and Sebastian in this scene, consider the intent that motivates their actions. Ultimately, I think there is a strong argument that Gonzalo's words are overly optimistic and unrealistic, perhaps even dangerously naive, and if Antonio and Sebastian had merely criticized Gonzalo on this account, then their actions might have been defensible. But such a reading runs contrary to the scene as Shakespeare wrote it.

The truth of the matter is that, regardless of whether or not you would agree with his words, Gonzalo is trying to be constructive. He is attempting to keep up their spirits by suggesting that things are not as bad as they look. Antonio and Sebastian, on the other hand, are not offering anything constructive at all; instead, they are mocking Gonzalo for their own shared amusement. It amounts to nothing more than pettiness.

This should not be surprising, considering that Antonio has already been established as the villain of the play, who had previously betrayed and usurped his own brother, Prospero, and very soon, under Antonio's influence, we will see Sebastian attempt to do the very same thing against his own brother, Alonso, the current king of Naples. These characters are not well-meaning or benevolent, and these interactions should be read with that in mind.