Well for one, no Arika Korps. Also, no occupation troops in Greece or maybe even Yugo. Men, resources, and leaders would be freed up for the Russian campaign. Although the outcome probably would not have been affected there, the campaign could only have been positively affected.

This also negates Italy as a front for the Allies to take on Germany. This would have serious reprecussions for any attempt into Western Europe, as the Allies would not have had the benefit of the combined arms experience North Africa and Italy gave them. Overlord nearly failed as it was, imagine greener Allied soldiers against a numerically stronger-than-historical coastal defense. That could have ended very badly.

In any case, Mussolini would probably have died in his sleep like Franco, not strung up by heels.

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"If your gonna buy the angel s**t, you might as well go for the zombie package as well."
-George Carlin