Three quarterbacks have started in the Super Bowl for two different cities.
Note the word "cities" instead of "franchises." That's because one quarterback won two Super Bowls for a franchise that switched cities.
That was Jim Plunkett, who won for the Oakland Raiders in 1981, defeating the Philadelphia Eagles, 27-10. The Raiders relocated to Los Angeles for the 1982 season, and Plunkett won again in 1983. The team moved back to Oakland in 1995. Plunkett is the only retired quarterback to win two Super Bowls and not get elected to the Pro Football Hall of Fame.
Craig Morton lost as the starting QB for the Dallas Cowboys in 1971, then lost as starting QB for the Denver Broncos in 1977.
Kurt Warner is quite familiar to Eagles fans, because two of his three Super Bowl trips came at the expense of the Philadelphia Eagles. As starting quarterback for the St. Louis Rams, he won the Super Bowl in 2000, after beating the Eagles in the NFC championship game, and lost the Super Bowl in 2001. He returned with the Arizona Cardinals in 2009, after again eliminating the Eagles in the NFC championship game.
See Wikipedia for a list of quarterbacks with multiple Super Bowl starts.