Battleborn's hyper-stylized space fantasy setting is populated by five ideological factions that must ultimately band together and send their "battleborn" champions to fight the Big Bad Evil Guy before he finishes destroying a universe already poised on the brink of annihilation.
Overwatch's near-future Earth sci-fi setting exists in a police-state that staved off an apocalyptic AI takeover thanks to the formation of an elite paramilitary unit known as Overwatch. With the cataclysm resolved, the UN-led Overwatch remained a peacekeeping force in the world until accusations of corruption and sedition turned the people of Earth against their saviors. Overwatch was disbanded, until... Well, we don't really know. But some bad guys are doing some bad things, leading to the call for heroes once more as our story begins.