Does rarity in games really mean a character is stronger?

When you see SSR, 5-star, or legendary characters, the first reaction is usually that they must be strong. But in some games, low-rarity characters can play a big role if well-trained, and some high-rarity characters might not be as good as expected in actual use. When you play games, do you prioritize training rare characters, or do you care more about the character's actual abilities?