The difference with Bitter Feud is that it designates two players, so that in a multiplayer environment, it would only affect two players. The cool thing about this, obviously, is that in a multiplayer setting, you need not be affected by the effects of the doubled damage.
As far as decks that actually have played Bitter Feud with any regularity, unsurprisingly Heartless Hidetsugu tops the list. Since his ability deals damage equal to half of each player's life total (rounded down), his deck absolutely loves any damage-doubling effect. Some Queen Marchesa decks have begun to include this card, too, despite Marchesa being a Commander you'd expect to be packing this sort of ability.
Bitter Feud is definitely a fun card in that it essentially puts two players into a life-and-death struggle. In 1v1 Commander, this is a particularly interesting card to consider, as long as the deck playing it can deal damage very quickly. It's a well-designed card for multiplayer Commander politics, and can be a deadly weapon in 1v1 Commander when deployed correctly.
While aggressive burn lists aren't extremely popular in the Commander format, they do exist. If ending games quickly by doubling damage is something you want to do, then Bitter Feud is definitely worth a look to play alongside other damage-doublers such as Furnace of Rath, Dictate of the Twin Gods, and the like.