Historically (I think) Cha-Cha developed from Mambo, which breaks on the 2 beat. Musically (an instructor pointed out) there is a difference between starting a movement on the downbeat (1) and the upbeat (2). That's the reason why Mambo and Salsa look different even though many of the steps are the same. Breaking on the downbeat makes it look more "laid back." Breaking on the upbeat makes it look "sharper" (more "upbeat").
Technically, the rhythm (slows and quicks) is the same but the timing (which beat of the music a movement starts on) is different. The instructor I mentioned demonstrated this by dancing a simple Waltz box, but stepping forward on the 2 beat instead of the 1 beat. And he was right; it looked different.