大败 and 大胜 are really lovable and hatable. They can be used with the same meaning but they are not always the same. Here are the tips for you to figure out how to differentiate 大败 and 大胜
When both are used as transitive verb, they have the same meaning:
defeat utterly; to put to rout. Examples:
甲队大败乙队。
甲队大胜乙队。
Team A defeated utterly Team B.
第一轮比赛中，她不到半小时就大败敌手。
第一轮比赛中，她不到半小时就大胜敌手。
She defeated her opponent in the first round in under half an hour.
When both are used as intransitive verb or noun, they have different meanings:
大败, intransitive verb: suffer a crushing defeat.
他们在那次战役中大败。
They suffered a crushing defeat in the battle.
大败, noun: a crushing defeat.
他们的领导决定调查大败的原因。
Their leader decided to investigate the reason for the crushing defeat.
大胜，noun: intransitive verb: win a big victory.
他们在那次战役中大胜。
They won a great victory in the battle.
大胜，noun: a big victory.
我们需要一场大胜。
We need a convincing victory.