Both main characters, Holmes and Poirot, use the powers of intellectual deduction to solve crimes. Both also are attended by assistants whom they underestimate and verbally abuse. Both are also intellectual snobs. Holmes is a cocaine abuser and a scientist, while Poirot is just a natural at deduction. Doyle's novels are set in England, while Christie has her characters traveling wherever crime may be: i.e. Mystery on the Orient Express, Murder in the Mesopotamia and Murder on the Nile. Both authors killed off their serial detectives and wrote books with other characters. Those of Miss Christie's, such as Miss Marple, gained more popularity among readers than Doyle's other books. In literary circles, Doyle is considered an Author with a capital A, while Christie was always thought of as merely a commercially successful writer (female, perhaps?) I personally prefer Christie because her secondary characters are more than just stage dressing for the "great man" to pontificate before.
“Time is the best killer.”