Very interesting question. I don't think you could rank them exactly, but if we grant each one everything we possibly could, there's a few that would at least be in the running.
Red: The first and the original, Red has been spun recently as the true Pokemon Master due to completing the first Pokedex and capturing every known Pokemon at the time. His biggest claim to the title is having the highest level Pokemon team in the entire main line series, and catching one of the most powerful Pokemon of all time, Mewtwo.
Gold: Not too many notable accomplishments, but the fact that he hiked his way to the top of Mount Silver and beat Red at his own game is telling enough. As far as we know, it's the only canonical loss that Red ever had until very recently in Sun/Moon.
Lucas/Dawn: Beating Cynthia is probably a big enough accomplishment on its own, but the biggest thing that keeps them in the running is their triumph and potential capture over the god of Pokemon himself, Arceus. That's a huge accomplishment.
Sun/Moon: It takes a pretty big badass to found a Pokemon League and be its first champion, but just like Gold, the fact that they were potentially able to defeat Red puts them higher up than others.
