While obviously they've crossed over tons of times since ... the characters were created in different eras, and their 'worlds' reflected and continue to reflect that difference to some degree.
Way back in the day, super heroes were typically alien (Super Man), tech/training (Batman), or accident (Fantastic Four, Spiderman, etc), basically because they took their cues from the sci-fi of the time. The deeper point your getting at though is the comic story telling was just simpler back then in terms of societal issues. It was much more black/white, good/evil with much less in terms of discussing deeper issues. Basically political propaganda versus communism (Superman and especially Captain America) was as far as they would go.
Stan Lee came up with the idea of mutants as a reaction to the fear of nuclear/cold war. The genetic mutations that created them are due to background radiation from nuclear testing. Part and parcel to this era however was the implications of the holocaust. The story telling got much deeper in terms of allegory, and continued to evolve along with then/now-current social commentary - racial issues, homosexuality, etc. Basically the mutant 'stigma' is allegory to the issues of the day.