I had thought that 'splitting' was the earlier form, in the sense of something splitting into two identical copies. This was the form my parents used, long before the satirical British TV show Spitting Image, which I thought was an altered spelling. It seems, however, that 'spitting image' is older than 'splitting image', and comes from an even earlier form 'spit and image'. Maybe 'splitting image' was influenced by the idea of a 'split image' in a camera.

Any comments?