Most things indicate that the Alliance won the Darkshore Warfront. Nathanos is no longer at Darkshore (having headed back to Zandalar before the Battle of Dazar’alor, and then we see him for Nazjatar before he goes back to Orgrimmar, and he doesn’t show up in the Alliance version of the Darkshore Warfront, either). The Horde’s version of the warfront is set right after the Alliance intro questing since the Horde has to save Belmont, and since that’s always the case and generals don’t change like at Arathi it would seem this is a gameplay mechanic like repeating dungeons rather than battlegrounds (Belmont also doesn’t show up in the Alliance version of the Darkshore Warfront, so it’s not like the Alliance players recapture him every time, either).
And even outside the Darkshore Warfront we have support that the Alliance won:
And then Nathanos says the Alliance is winning on all fronts after Dazar’alor, which would have included Darkshore.
The Heroic Darkshore Warfront didn’t even change anything mechanically like the Heroic Arathi Warfront did. The Heroic versions of the warfronts are purely gameplay, no more lore than running Heroic Dungeons again after running then in Normal mode first.