I think the Allies win.
The Nazis would be massively distracted by trying to 'cleanse/pacify' the USSR, and wouldn't be able to shift everything west.
Would it be a blood bath? Oh, ya.
But I suspect that, since the Allies would have air superiority or even supremacy, that they could hold and expand any beachhead that they actually established. If they tried 5 beaches, as OTL, I suspect at least one would be pushed back into the sea, and at least one would establish a solid beachhead. But. Oh yeah. Blood bath start to finish.
Expansion out of the beachheads might be slow (more like the OTL Italian campaign than OTL Normandy), but the US is essentially unbeatable if it tries hard enough.
Then they is what to do with Germany this time around, and what use to be the USSR.