I love both of these characters, but you don’t see many Mr. Moto movies on TV anymore…nor are they radily available on DVD. anyway, was the Mr. Moto character made up in response to the popularity of the Chinese-American detective? How many Mr. Moto movies were made, and when did the series end?
Actually, Peter Lorre was fairly convincing as a japanese…was Warner Oland ever mistaken for a chinese guy? 
Charlie Chan came first and was a success, so Mr. Moto was at least partially connected to it (they were both made by the same studio).
According to Maltin, nine Mr. Moto films were made – eight with Peter Lorre in the 30s and an attempted revival in 1965 with Henry Silva.
Mr. Moto’s Last Warning is readily available on DVD, usually in cheap boxed sets of 30s mysteries (I have it bundled with some Bulldog Drummond films). The copyright was not renewed on it. The other films are under copyright
Both detectives were published in book form long before they had movie versions made.
Earl Derr Biggers started the Charlie Chan books with The House Without a Key in 1925. The first movie with Warner Oland was 1931’s The Black Camel. There apparently were three silent films earlier but I don’t know anything about them.
Biggers died in 1932. John Marquand, already a minor novelist and short story writer, responded to a request from the Saturday Evening Post to take over writing stories about an Oriental sleuth. The first Mr. Moto book was No Hero in 1935, with the first movie two years later.
Unusually, Marquand wrote serious novels alternately with the Moto books. His The Late George Apply won the Pulitzer Prize in 1938.
Peter Lorre is Peter Lorre, but the Chan movies were, by and large, much better films.
They may not be great but they do seem to be readily available on DVD.