Well, Red's in the Pokemon manga, which I've never read, so I don't really know why he's better than Ash.
Although Ash tends to have made some very stupid mistakes in the original Pokemon seasons like trying to capture Pidgeotto (a bird) with his Caterpie (a caterpillar). Then Ash uses Pikachu which is what he should've done in the first place. Misty chews him out for using a bug against a flying type "Birds eat bugs, Mr. Pokemon Master!".
And whenever he battles another trainer like a gym leader, he usually purposefully puts himself at a disadvantage. Even though it is possible for a disadvantaged Pokemon to win, it's still not a bright idea.
Also, even though Ash does fairly well in the Pokemon League tournaments, he always ends up losing. He's only won once during the Orange Islands.
Ash did get better in Hoenn and Sinnoh, but starting with Unova, he reverted back to his dumbass self in the original season.