The 19 QB's in the chart below are the greatest QB's of the Modern Era (post-1960). Of the former players on that list, all are in the Hall of Fame but Ken Anderson and Ken Stabler and both men have good cases for enshrinement (at least Anderson does in my opinion). Of the three active players, Favre, Manning and Brady will all be in the Hall one day.
Despite the collective greatness of these 19, we see how very difficult it is to win road playoff games. As a group these 19 QB's won barely a third of their road playoff games. Only four of the QB's have at least a .500 winning percentage in their road games: Starr, Staubach, Elway and Brady. And Starr has a unique accomplishment among QB's of the modern era: his two road wins both came in NFL Championship Games! Starr (my pick for the greatest QB of all-time) is the only QB of the modern era to win two championships on the road (at New York in 1962 and at Dallas in 1966).
Of course, no QB today could hope to match that accomplishment. Since 1970, all NFL Championship Games have been played on neutral sites. You may have heard of a little game known as the Super Bowl. So the next closest thing a QB can do to match (or better) Starr would be to win two conference championship games on the road. And strangely enough, the other three modern-era QB's with winning road playoff records have all done just that. Staubach beat the Rams in Los Angeles in both the 1975 and 1978 NFC Championship Games while Brady beat the Steelers in Pittsburgh in both the 2001 and 2004 AFC Championship Games. It's interesting that each man's second road triumph came three years after his first with the same opponent serving as his repeat victim. Elway took a more unique path, beating Cleveland in 1986 (the Drive) and then beating Pittsburgh eleven years later. Pittsburgh sure seems to have lost an unusual number of AFC title games at home.
If we include QB's of the pre-modern era, we do find one other QB who matched Bart Starr's accomplishment. Chicago Bear great Sid Luckman won NFL titles in Washington in 1940 and in New York in 1946. Let's see Kyle Orton do that!