Nemesis: Martian Manhunter
Other Major Foes: None
Appearances: 7 comics
Powers: Telepathy, flight, shape-shifting, Laser Vision, nigh-invulnerability, invisibility, intangibility, and superhuman strength/ physique/ senses/ reflexes/ endurance..
D'Kay was a surviving Green Martian madwoman serial killer who tried to mind control the Martian Manhunter into loving her and repopulating Mars. Instead, he roasted her in the sun.
Lose: Bette Noir (3-14); Thantos (5-9)
Other Major Foes: Superman, Brainiac
Appearances: 150+ comics, animation, and live action television.
Powers: Telepathy, flight, Optical Force-Beams, force fields, telekinesis, nigh-invulnerability, and superhuman strength/ physique/ senses/ reflexes/ endurance.
Maxima was the empress of the planet Almerac and its intergalactic empire when she chose Superman as her perfect mate. When the Man of Steel rejected her, violence ensued. Despite the blood shed in her name, Maxima became a reluctant heroine and member of Extreme Justice, where her advances on alternative sperm donors Captain Atom and Amazing Man never produced an heir. Starbreaker demolished Almerac, and Maxima herself perished in battle against Brainiac.
On paper, Maxima is the clear winner, based on her years trying to force the sexy on Superman in a not-too-gentle fashion. However, her initial overwhelming power levels were dismissed as belonging to some sort of murderous simulacron, and her time on a lesser Justice League team needing help against chromium cornballs mangled her reputation. Meanwhile, D'Kay laid a serious telepathic mind____ on the Alien Atlas, then she held up as he battered her quite savagely for it. Quite the toss-up, then, though I will say Maxima's a lot more fun and a lot less aggravating.