They are opposites. They express what a person would like for another person--ill will vs. good will.
Curse someone these days, and most people shrug it off. They might get angry, and return the favor, stringing expletives damning someone to hell, or hammering them with the "f-word." (I can't help it. I just can't say it. Don't judge. :-) There are a lot of curses that seem to have formed a new language for people.
But when someone offers a blessing, "God bless you," it can sound so trite. It is so hard to say, and it is so hard to hear. Why do you suppose that is? Is it because the other person seems holier than thou? Is it because we don't feel we deserve someone's good will? Is it because, it is often said by people you don't even know in the same way someone would say, "Have a good day?" Of course, when you sneeze, people welcome "Bless you" from people they don't even know. But can you offer your blessing in other ways, that don't say, "Bless you!"
You can say, "I hope you are feeling better soon!" or "Good luck on that job interview! Knock 'em dead!" or "I hope you have a wonderful vacation!" But there are no colorful blessings. The only canned blessing we have is, "Bless you."