Commodus is pretty well known actually, at least as far as acounts go, we have stories from Cassius Dio about him killing rivals and killing things in the Coliseum in his book 73. He so badly idolized the gladiators so he killed animals himself and fought fake fights in whish "commodus received a million sesterces from the gladiatorial fund each day" (73.9.3). He made senators shout things about how great he is (73.20.2). Also he tried to scare them,

"Having killed an ostrich and cut off his head, he came up t where we were sitting, holding the head in his left hand and in his right raising aloft his bloody sword; and though he spoke not a word, yet he wagged his head with a grin, indicating that he would treat us in the same way. And many would have perished by the sword on the spot, for laughing at him (for it was laughter rather than indignation that overcame us), if I had not chewed some laurel leaves... so that in the steady movement of our armies we might conceal the fact we were laughing" (73.21.1-2).

He was eventually assassinated because of his musings of assassinating he close family members and advisors were simply left on the table.

As for Caracalla, we do have a bit on him, but after his death he suffered a "damnatio memoriae" a damning of his memory which meant it was illegal to mention him, and that anything of him must be destoryed, such as statues or books. there are cases of statues being simply redesigned into the new emperors.

Why didn't the others suffer the same damning? well they were all succeeded by new dynasties whereas the Severan Dynasty continued after Caracalla, so damning him saved the family face. In the Case of Titus replacing Nero, he would have wanted people to know his transgressions against the citizens and Rome.