This one's not even close.
The Philadelphia Phillies have significantly more playoff experience than the Washington Nationals. The Phils have made the playoffs for five straight years, and went to the World Series in both 2008 and 2009.
There are still several key contributors left from the 2008 World Series championship squad (pictured), including Cole Hamels, Ryan Howard, Jimmy Rollins, Chase Utley and Carlos Ruiz. The pitching staff includes more playoff veterans who were added since 2008, including Roy Halladay, Cliff Lee and Jonathan Papelbon.
The Washington Nationals only have two players who have won a World Series ring: Edwin Jackson with the 2011 St. Louis Cardinals and Jayson Werth with—ironically enough—the 2008 Philadelphia Phillies.
The bulk of the Nationals roster has never even seen the postseason, including starting pitchers Jordan Zimmermann and Gio Gonzalez, relief pitchers Drew Storen and Tyler Clippard, and position players Ryan Zimmerman, Ian Desmond, Danny Espinosa, Michael Morse, Kurt Suzuki and Bryce Harper.
These young Nats will learn playoff baseball the hard way when they play the Phillies.