Thersites is a fascinating character. As a Greek slave, he occupies the lowest rung of the ladder in Trojan society, and yet he seems to given words of immense wisdom as he comments upon the various foibles and idiosyncracies of those characters who are placed way above him. Whilst his language is often rather ribald and abusive, he is the only character who can be said to be a moralist in this play, and seems to express the views of Shakespeare as he provides a somewhat sarcastic and bleak commentary on the character failings of those who, in society's eyes, at least, are above him. Note his famous comment in Act II scene 3, when he argues, based on the devolution of the love between the two title characters, that "all argument is a whore and a cuckold." Thersites is therefore used to point out the base and mean nature of the characters that we would expect to be moral exemplars.
Aaron, on the other hand, seems to be a massive bundle of contradictions. Whilst he seems to be the embodiment of evil, playing the role of villain with great gusto and deliberately perpetrating terrible events in this play, at the same time he is an incredibly engaging character that draws the audience in to his confidence through his soliloquies. Whilst his evil deeds are clear, at the same time we are prevented from regarding him as simply a monster through the humanity that he evinces in his love of his son. Note how he is swift to discard Tamora and his role as her lover with the various rights and privileges that this gives him to seek his child's safety. In the same way, he is willing to reveal the many wrongs committed against the family of Titus Andronicus in exchange for the life of his son. Every time we are tempted to consider him as a character consumed completely by evil, such instances remind us of his humanity.
Perhaps the central similarity between these two characters therefore lies in the way that both defy our expectations. Thersites is a character who shows himself to be more noble than the lords of Athens and Sparta, whilst Aaron seems to delight in vexing our ability to make a judgement on his character.