City of Dragons takes place in San Francisco's Chinatown in 1940, and the heroine is a cynical, hardened private investor, former escort, and nurse who lost the love of her life in the Spanish Civil War. She has friends in the press, but the police dislike (even try to frame) her. She doesn't get along with her father, and grew up without a mother. She gets beat up badly by gangsters in her attempt to solve several murders that involve drugs, human trafficking, and embezzlement.
This Dame for Hire is set in New York in 1943, and the heroine is a wise-cracking assistant to a private investigator who takes over his business when he goes off to war. She has friends on the police force, and her best friend is a psychic who sometimes helps with her cases. She doesn't get along with her father, and grew up without a mother. She gets beat up by a suspect in her attempt to solve several murders that involve actors, academia, and abortions.
Because I read them back-to-back, it's a little hard to see any major differences. I appreciated the gritty portrait of San Francisco in Dragons; I appreciated the consistency of slang in Dame ("ya" for "you" everywhere, "g" dropped from "ing", etc). I didn't really love either book, and neither was very riveting, but they did make for decent late-night reading on ridiculously warm February nights.