Over the past decade, there have been five occasions, in which there was discrepancy between the Best Director and the Best Picture Oscars:
1998:
Best Director: Steven Spielberg (Saving Private Ryan)
Best Picture: Shakespeare in Love (directed by John Madden)
2000:
Best Director: Steven Soderbergh (Traffic)
Best Picture: Gladiator (directed by Ridley Scott)
2002:
Best Director: Roman Polanski (The Pianist)
Best Picture: Chicago (directed by Rob Marshall)
2005:
Best Director: Ang Lee (Brokeback Mountain)
Best Picture: Crash (directed by Paul Haggis)
2013:
Best Director: Ang Lee (Life of Pi)
Best Picture:
2014:
Best Director: Alfonso Cuaron (Gravity)
Best Picture 12 Years a Slave (directed by Steve McQueen)