When viewers meet Joffrey Baratheon in HBO's Game of Thrones, he seems like a little bit of a pain. He's spoiled and entitled, downright rude to people, and doesn't take criticism well. Things go from bad to worse as they find out that he's actually the son of Cersei and Jaime (brother and sister, and both dangerous in their own ways), and the acts he commits get increasingly worse. Even Jaime, who's no saint, seems pretty appalled by him at points while Cersei thinks he can do no wrong.
But as terrible a king as he is, the man on the throne before his 'father' Robert Baratheon was pretty bad too. Aerys Targaryen II is dead long before the show begins, but the stories that come from him are enough to send chills up anyone's spine.
So who's worse?
Joffrey: Wasn't Actually In Line For The Throne
The fact of the matter is that Joffrey actually has no right to be sitting on the throne, good or bad. He's there because he's ed off as the usurper Robert Baratheon's son, but he's actually the product of Jaime and Cersei Lannister, like his brother and sister. Knowing they would all be executed for anything else than the truth — and wanting her son to be king — Cersei is happy to play along, acting as if he's Robert's. He ascends to the Iron Throne after Robert's death, and shouldn't be there.
Aerys: Abusive, Ill-Advised Marriage
It's not just the Lannisters who have twisted relationships between siblings. Actually, the Targaryens are pretty famous for it.
As is a tradition in the dragon family, Aerys was married to his sister, Rhaella. It was a pretty terrible marriage. We hear about some of it from Jaime Lannister, who recalls how abused Rhaella was and how she would cry for help. Jaime reflects on the fact the Kingsguard had to vow not to interfere. Safe to say, Aerys wasn't just a bad king, but a terrible person.
Viserys came out of the deal extremely damaged, though Rhaegar and Daenerys at least miraculously seemed to be decent people — for a time.
Joffrey: Abusive To Sansa
Joffrey isn't a stranger to abuse. He may never marry Sansa Stark, but he does treat her terribly. He has his Kingsguard hit her, humiliates her frequently, and even intends to beat her and threatens her with a crossbow in front of the entire throne room. Sansa escapes this entire marriage, but it's pretty obvious the abuse might have escalated, especially after some appalling comments Joffrey makes at her wedding to Tyrion.
Aerys: Didn't Trust Anyone
Aerys didn't trust anyone — period. As a result, he went through Hands and advisors before executing each and every one, convinced they were betraying him.
It's not only awful because he was executing them but he was ruining his chance of getting real, valuable advice on ruling because everyone was scared to tell him the truth, instead telling him what he wanted to hear.
Joffrey: Discarded The Best Advice He Had
In the series, the best advice Joffrey has doesn't come from his mother, Cersei — it comes from his uncle, Tyrion and his grandfather, Tywin. Tywin may not be a nice person or even a good father, but he knows a thing or two about ruling and tries to advise Joffrey. Joffrey discards his advice, certain he knows how to do this on his own.
At least he didn't get as far as executing people though.
Aerys: Broke The Law To Execute People
Not only did Aerys execute people, he did it awfully.
He would allow his victims to demand a trial by combat and would choose fire as his champion rather than another person. Then, he would burn the person alive rather than allowing them to engage in a fair fight. Jaime Lannister, in particular, recalls the gruesome details of their death and how Aerys laughed.
Joffrey: Humiliated People For His Own Pleasure
Joffrey doesn't execute people by wildfire, but he does humiliate them — in particular, his uncle Tyrion, who has only ever tried to help him. It's a grotesque power display that makes everyone uncomfortable on multiple occasions and despite his to-be queen, Margaery, trying to pull him away, he isn't deterred.
Both: Murderers
The truth of it is though, they're both murderers. Joffrey has people executed and kills two women by his own hand later in the series with a crossbow, purely for his own amusement — after having one beat the other. Aerys murders a lot more people, but who's to say Joffrey would never have gotten that far if death hadn't interrupted him?
Aerys: Would Have Blown Up King's Landing
Aerys, however, had a plan to blow up the entire city. He stashed wildfire all over it and was planning on igniting it so that everyone in the city would be burned alive, and his opposition in war could never rule over the capital of Westeros. He was stopped only when Jaime Lannister discovered his plan and slit his throat (or, in the show, literally stabbed him in the back).
Worst King: Aerys
Joffrey may have gotten as bad as Aerys — but we'll never know, since he died before viewers could see. Aerys, however, murdered a countless amount of people and seemed to take great pleasure in doing so. Joffrey was a bad king, but far more people would have suffered torturous deaths under the man infamously known as the Mad King.