Pitter-patter is more girly and banal. Jibber-jabber hints at the far away, mysterious and exotic. Carl Sandburg could write about pitter-patter, but Rudyard Kipling would take up jibber-jabber.
I like it. From “Big Bang”. My favorite is when Sheldon starts explaining what jibber-jabber is and Penny says, “On my gosh Sheldon is going to jibber-jabber about jibber-jabber.”