Women who can afford to breastfeed exclusively are at least middle class, usually upper-middle class. That comes with a whole set of advantages and other correlations. Studies that try to figure out breast feeding advantages have to try and control for these things, but it's hard.
Here's what we know for sure: Breast feeding reduces infections in the child. It's a small, but detectable amount. And I do mean a small amount. Between six mothers that exclusively breast feed an infant for six months, on average one of those children will have one fewer infection during that time.
Everything else is up in the air, and if it has an effect on anything else (like intelligence) it's tiny. Save your energy for reading to the child and playing games with them, which definitely helps intelligence.