One a monarch of an alien world seeking immortality, the other a disgruntled scientist seeking fortune. Each faced off against their universe's mightiest heroic teams more than once backed by mindless minions.
Queen Zazzala of the planet Korll sought out the serum to gain immortality, and was drawn to Earth-One when her bee men were defeated by the Justice League of America. Employing them as pawns, she gained mastery over death but at the cost of her mobility. Repeatedly using actual insect humanoid of her world, real bees as well as mutating her foes, this self-styled Queen Bee never succeeded in regaining a fully functioning body in the long term.
Elmer Pane came from more modest backgrounds, himself a mere scientist of Earth-Two yet with great aspirations. Developing the means to utilize hormones in the transform his henchmen into termite/spider/grasshopper/fly/bee men, Pane as the King Bee instigated a crime wave that drew the attention of the Justice Society of America. Defeated but not dejected, he was later recruited by time traveler Per Degaton to aid the villain in conquering the world a year before he actually first appeared. Once more he faced defeat and returned to his own version of immobility, a prison cell, never to reappear.
While Queen Bee limited herself to the bee-men of her world and humans transformed into minature bee-men, King Bee created a whole host of insect allied. Besides his most recurring henchmen, the hornet-men, he also had other insectoids that paralleled villains on Earth-One. These included grasshopper men of the Outsider as those of King Bee. And the spider men, borer men and fly men of Earth-Two all had analogues on their parallel world in alien races that combated the Justice League.
Eventually, both of these royal pests needed to ally themselves with fellow felons to defeat their greatest obstacles, and so they ended up forming alliances with several supervillains in a scheme to defeat the League and Society individually. Queen Bee's Anti-Justice League would be a precursor for the the more famous, or infamous, Injustice Gang of the World that would shortly follow. Allow in her case, she assembled so prime talent to counteract the Justice League, at least until Superman discovers her scheme to ambush each of his teammates by him or herself and turns the table on this assemblage of evil.
By way of contrast, King Bee was a mere recruit in Per Degaton's plan, as that time traveling terrorist recruited several supervillains from various eras to corner and conquer the Society members in smaller teams, thereby removing his threat to capturing this period of time on the verge of world war. Three heroes escaped and were able to enlist the aid of other mystery men in defeating the King and his cronies, who ended up being dispatched from whence they came with none the wiser.