I noticed that 決闘 and 勝負 are both translated as “duel” but I wondered if there are any underlying differences in meaning between the two words.
決闘 specifically refers to this tradition to protect one's honor, fought with rapiers, pistols or such. It usually ends with one of the participant's death. Basically this is something in the past (at least in developed countries), and you won't see this outside of wild-west movies or dramas set in the middle ages. This kind of dueling was mainly practiced in Europe and the US, and the word 決闘 also typically refers to Western ones. Japanese samurais also occasionally did similar things, but they may tend to be called 果たし合い.
勝負 is a much broader term that encompasses "match", "game", "(card game) duel", etc.
決闘 is used for the one-time win/lose situation to be involved in the honor. It is especially used to refer the stage damage/being damaged in a direct way.(i.e. French mathematician Évariste Galois are believed to have dueled for his fiancée, Kojiro Sasaki and Musashi Miyamoto are believed to have dulled for their art of sword mastery in Ganryu island and so on.)
The honor of both parties will maintain depends on the performance of the duel. Kojiro Sasaki and Musashi Miyamoto are both known to be sword mastery.
勝負 is a much more broad term and may have similar nuance with the duel though, it basically is used to decide win/lose in an indirect way. It is used to describe for using a lot of energy to compete though, it is not necesarilly implying for the honor. It can be used for the game of winning the goods like bingo.