They both became ruthless and brutal by horrible events that occurred in their past (Cletus Kasady born in the Asylum Ravencroft and throughout his childhood he was mistreated and despised by the people around him which eventually turned him into a psychopath and Doosmday was originally a baby who was used in an experiment that forced him to die over and over again and that caused him had a hatred for all living beings)
Both Always Return and Evolve to become stronger and both are the strongest members of their race and they overcame the weaknesses and gained immense power. With Carnage losing his weakness of first and sound and Doomsday losing his weakness to practically everything Due to their perseverance, regeneration and their ability to adapt and become stronger.
Both managed to defeat the strongest team of heroes of their respective universes (The Avengers and the Justice League) and have been a threat to the world multiple times.
Even both at a certain point in their history tried to be Heroes but that didn't turn out well for them.
Both are so unstoppable that not even death can stop them (Carnage always manages to come back from death and even while in hell he manages to devise a plan to become the new king of the Symbiotes and Doomsday always resurrects stronger than before).
