The golden age and silver age had characters that mirrored one another, from their appearance to their disposition to their personal adversaries. Such was the case for Merlyn the Magician and Professor Merlin, each of whom having faced their world's Green Arrow and his allies.
Now Merlyn of Earth-One was not a magician, he was an ace archer who made trick shots that seemed as if by magic, when in fact they were simply skill. Armed with equipment from the League of Assassins and sent on a mission by its leader the Sensei to destroy the Justice League of America, Merlyn had a particular grudge match against the Green Arrow who usurped his World's Greatest Archer reputation. At the end of that conflict, the Arrow proved he was better.
As for Professor Merlin of Earth-Two, he wasn't so much an athlete with a bow and arrow as he was a master strategist. Using equipment he stole along the way, he crossed paths with Green Arrow and Speedy, and was finally defeated by the pair. He had a return engagement when Merlin joined the Hand's Five Fingers to battle the Arrow and his teammates known as Law's Legionnaires.
Once more, Merlin was vanquished, which also happened when Meryln later reappeared in Metropolis to face Black Lightning. After that second defeat, Merlyn followed the career path of his counterpart Merlin, and vanished from sight!