This pair can mainly be dealt with together, since nearly all of their lines are together, and their action is matched. They're also in similar positions: both are traitorous younger brothers. Antonio is Prospero's brother, who betrayed him to have the dukedom; Sebastian is younger brother to King Alonso of Naples, and is interested in stealing Alonso's throne. They work well together because Sebastian is prone to fooling around in a mean-spirited way and Antonio earns Sebastian's trust and respect by also being a horrible human being. When Sebastian is moved to murder his own brother, it is at the suggestion of the traitorous Antonio.
In their last lines in the play, Sebastian and Antonio mock Trinculo and Stefano (who are basically their reflections). They show they have learned absolutely nothing, have no remorse, and do not wish to be forgiven, because they see nothing wrong with themselves. Their plot against the King, their lack of remorse, and their wickedness in general characterize them as bad seeds.
The entertaining part of this pair is their jesting with words and ideas. They have no boundaries on the horrible things they'll say, and they make fun of everything, usually cleverly and with great effect. Basically, we find them disgusting, but fascinating to watch.