They mean the same but they feel different. #1 paints a picture. #2 states a fact.
"Losing" is an adjective, like "happy". Grammatically, the sentences
"He was losing" and
"He was happy"
have the same structure. Both describe the person using adjectives. Adjectives paint pictures.
#2 uses a verb ,"lost", instead of an adjective. Verbs ACT rather than describe. When you use a verb, something happens: "he lost!". That is not a picture. It is an event that happened.
Many people call the adjective "losing" a tense ("past continuous", or whatever). That's not my way of looking at it, but it's fine if it helps you. But continuous motion over time is like a picture - it is something that you can visualize, so in that sense these two ways of explaining "losing" are really similar.
Whether to use #1 or #2 depends on what you are trying to do. To tell a story, you must use verbs. You cannot rely on adjectives. However, you also want to use adjectives because a story without descriptions is too factual. Adjectives help your imagination. You need both. The structure of a story is built with verbs, but the adjectives are needed embellishments.