CSI New York is the more serious of the three.
CSI is serious but it does have quite a bit of more humor than the other series . They usually have a few episode a season that are more comedic in nature.
CSI Miami is a huge chesefest. It's not very serious even when it tries to be serious. It seems almost like a show right out of the 1980's. Especially with Horatio Caine being less concerned about legalities than the characters on the other series. I remember one episode that ended where it was very obvious that Caine was going to beat the living shit out of a guy as the show faded to black. Nothing really came out of it. It's just a really cheesy show. It's over the top So I enjoy it for the cheesiness.