I’ve been giving some thought to "The Decisive Moment," the title chosen for Cartier-Bresson’s book by his American publisher, in 1952. I think it was an unfortunate choice of words that has often led us astray, by suggesting that a distillation of reality has been caught in such a moment.
In France, the elegant little book was titled, "Images à la Sauvette." Translated colloquially, it means "Images on the Run," which is a more expansive concept. It allows us to consider a fleeting facial expression, for example, or momentary body language.
Great street photos, or any great photos "caught on the run," evoke emotions such as humor or pathos. They may in some sense be "decisive," but that’s not the point. It’s their evocative content-cum-composition that makes them great.