Riggs was a member of the U.S. Special Forces until 1969, receiving specialized training. He fought in Vietnam as a CIA-employed assassin and now he regularly puts himself in danger in hopes someone will take him out. He's an alcoholic who struggles to get a grip after the tragic death of his wife, Victoria, in a car crash.
Murtaugh is an experienced police officer working for the LAPD. He also fought in Vietnam, and now he tries to work hard to provide for his family. He's an exhausted, by-the-books cop who wants desperately to retire but is somehow always being roped back in.
Take your pick: