In literal ways "tug-of-war" would be a context in which the contestan pull against each other by pulling a rope.
Thus in literal ways, tug-of-war isn´t a "queda de braço", but "um cabo de guerra".
Anyway, in non-literal ways it could be said that someone had "uma queda de braço" by saying that there was a tug-of-war (but in non-literal ways). Metaphorically speaking - by trying to gain the same "prize" or goal. Let´s imagine a couple is in the process of divorce and get playing a tug-of-war for the dog. In this case it´s a battle (in Portuguese could be also a metaphorical "queda de braço" - briga, batalha).