With duplicates removed:
List A					List B
A Streetcar Named Desire		Alien
All About Eve				Aliens
Annie Hall				Amadeus
Best Years of Our Lives			American History X
Bonnie and Clyde			Back to the Future
Deer Hunter				Departed
Duck Soup				Eternal Sunshine of the Spotless Mind
General					Forrest Gump
Gold Rush				Full Metal Jacket
Graduate				Goodfellas
Grapes of Wrath				Gran Torino
High Noon				Inglourious Basterds
Intolerance				L.A. Confidential
It Happened One Night			Leon
Jaws					Memento
MASH					Modern Times
Midnight Cowboy				Paths of Glory
Mr. Smith Goes to Washington		Pianist
Nashville				Raiders of the Lost Ark
On the Waterfront			Requiem for a Dream
Philadelphia Story			Reservoir Dogs
Rocky					Saving Private Ryan
Searchers				Terminator 2: Judgment Day
Shane					Third Man
Sound of Music				Up
Sullivan's Travels			WALL-E
				
Complete lists:
List A					List B
2001: A Space Odyssey			2001: A Space Odyssey
A Streetcar Named Desire		Alien
All About Eve				Aliens
Annie Hall				Amadeus
Apocalypse Now				American History X
The Best Years of Our Lives		Apocalypse Now
Bonnie and Clyde			Back to the Future
The Bridge on the River Kwai		The Bridge on the River Kwai
Casablanca				Casablanca
Chinatown				Chinatown
Citizen Kane				Citizen Kane
City Lights				City Lights
The Deer Hunter				The Departed
Double Indemnity			Double Indemnity
Dr. Strangelove				Dr. Strangelove
Duck Soup				Eternal Sunshine of the Spotless Mind
The General				Forrest Gump
The Godfather				Full Metal Jacket
The Godfather: Part II			The Godfather
The Gold Rush				The Godfather: Part II
The Graduate				Goodfellas
The Grapes of Wrath			Gran Torino
High Noon				Inglourious Basterds
Intolerance				It's a Wonderful Life
It Happened One Night			L.A. Confidential
It's a Wonderful Life			Lawrence of Arabia
Jaws					Leon
Lawrence of Arabia			The Maltese Falcon
The Maltese Falcon			Memento
MASH					Modern Times
Midnight Cowboy				One Flew Over the Cuckoo's Nest
Mr. Smith Goes to Washington		Paths of Glory
Nashville				The Pianist
On the Waterfront			Psycho
One Flew Over the Cuckoo's Nest		Raging Bull
The Philadelphia Story			Raiders of the Lost Ark
Psycho					Rear Window
Raging Bull				Requiem for a Dream
Rear Window				Reservoir Dogs
Rocky					Saving Private Ryan
The Searchers				Singin' in the Rain
Shane					Sunset Boulevard
Singin' in the Rain			Taxi Driver
The Sound of Music			Terminator 2: Judgment Day
Sullivan's Travels			The Third Man
Sunset Boulevar				To Kill a Mockingbird
Taxi Driver				The Treasure of the Sierra Madre
To Kill a Mockingbird			Up
The Treasure of the Sierra Madre	Vertigo
Vertigo					WALL-E