Not a geneticist, but some research leads me to believe it would be akin to mating with your identical twin, rather than to cloning yourself. That is, less genetic variation than mating with your fraternal twin, but still achieving the recombination effect which makes sexual reproduction advantageous over asexual reproduction.

That said, I seem to recall hearing once that "higher organisms" will fail to produce viable offspring via self-insemination, but I have no idea how accurate that is.

Comments on Difference Blog by Dan4th: The origin of sexes