Grandiose Historic/Dramatic Epics and in last 50 years, those with ethnic themes have tended to win over popular/entertaining and classic/innovative faire:

Anything by Chaplin:

1931 City Lights loses to Cimarron

1936 Modern Times loses to The Great Ziegfield

1940 The Great Dictator loses to Rebecca

Most Anything by Hitchcock (except Rebecca)

1951 Strangers on a Train loses to An American in Paris

1958 Vertigo loses to Gigi

1959 North by Northwest loses to Ben Hur

1960 Psycho loses to The Apartment

Also

1944 Double Indemnity loses to Going My Way

1948 Treasure of the Sierra Madre loses to Hamlet

1950 Sunset Boulevard loses to All About Eve

1953 Shane loses to From Here to Eternity

1967 The Graduate loses to In the Heat of the Night

1980 Raging Bull loses to Ordinary People

1987 "Princess Bride" loses to The Last Emperor

1989 Dead Poets Society loses to Driving Miss Daisy

1998 Saving Private Ryan loses to Shakespeare in Love