I don't have Internet access on my computer atm, but the short version is that in the UK at least, the decisive change occurred around the 18th century. Pistols presented a more even playing field than swords, the highly codified rituals surrounding it made it fit in with the emerging middle class sensibility of 'civilised' masculinity. Boxing also emerged around this time but as a considerably more working class affair, as it was seen as beneath refined gentlemen.

Good reading on this is R Shoemaker, The London Mob.