With the release of White House Down, a lot of conversations lately bring up past occurrences where two very similar films were released around the same time. Here's a breakdown and comparison of all the ones I could think of. Let me know if I missed any (theatrical releases only, not those rushed direct-to-video ripoffs; and only those released very close to each other - not like years apart)
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Olympus Has Fallen - 3/22/13
$98.7M
RT score (critics/audience): 47/73
White House Down - 6/28/13
$TBD
RT score (critics/audience): 50/73
First Released: Olympus Has Fallen
Box Office Winner: TBD
Better Movie: close race, I would say Olympus Has Fallen
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Mirror, Mirror - 3/30/12
$64.9M
RT score (critics/audience): 49/45
Snow White & the Huntsman - 6/1/12
$155.3M
RT score (critics/audience): 47/54
First Released: Mirror, Mirror
Box Office Winner: Snow White & the Huntsman
Better Movie: Snow White & the Huntsman
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No Strings Attached - 1/21/11
$70.7M
RT score (critics/audience): 49/54
Friends with Benefits - 7/22/11
$55.8M
RT score (critics/audience): 71/66
First Released: No Strings Attached
Box Office Winner: No Strings Attached
Better Movie: Friends With Benefits
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Happy Feet - 11/17/06
$198M
RT score (critics/audience): 75/75
Surf's Up - 6/8/07
$58.9M
RT score (critics/audience): 78/64
First Released: Happy Feet
Box Office Winner: Happy Feet
Better Movie: Surf's Up (though neither is especially good)
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The Prestige - 9/1/06
$53M
RT score (critics/audience): 76/90
The Illusionist - 10/20/06
$39.8M
RT score (critics/audience): 74/83
First Released: The Prestige
Box Office Winner: The Prestige
Better Movie: The Prestige
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Capote - 9/30/05
$28.7M
RT score (critics/audience): 90/73
Infamous - 10/3/06
$1.1M
RT score (critics/audience): 72/60
First Released: Capote
Box Office Winner: Capote
Better Movie: Capote
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Madagascar - 5/27/05
$193.6M
RT score (critics/audience): 55/70
The Wild - 4/14/06
$37.4M
RT score (critics/audience): 19/53
First Released: The Wild
Box Office Winner: Madagascar
Better Movie: Madagascar (though The Wild is not bad)
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Chasing Liberty - 1/9/04
$12.2M
RT score (critics/audience): 19/61
First Daughter - 9/24/04
$9.1M
RT score (critics/audience): 8/49
First Released: Chasing Liberty
Box Office Winner: Chasing Liberty
Better Movie: Chasing Liberty
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Finding Nemo - 5/30/03
$339.7M
RT score (critics/audience): 99/82
Shark Tale - 10/1/04
$160.8M
RT score (critics/audience): 36/59
First Released: Finding Nemo
Box Office Winner: Finding Nemo
Better Movie: Finding Nemo
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Mission to Mars - 3/10/00
$60.8M
RT score (critics/audience): 25/33
Red Planet - 11/10/00
$17.5M
RT score (critics/audience): 14/31
First Released: Mission to Mars
Box Office Winner: Mission to Mars
Better Movie: RT scores say Mission, I say Red Planet
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Truman Show - 6/5/98
$125.6M
RT score (critics/audience): 95/82
EdTV - 3/26/99
$22.4M
RT score (critics/audience): 64/31
First Released: Truman Show
Box Office Winner: Truman Show
Better Movie: Truman Show
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Saving Private Ryan - 7/24/98
$216.1M
RT score (critics/audience): 93/92
Thin Red Line - 1/15/99
$36.4M
RT score (critics/audience): 78/75
First Released: Saving Private Ryan
Box Office Winner: Saving Private Ryan
Better Movie: Saving Private Ryan
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Antz - 10/2/98
$90.6M
RT score (critics/audience): 95/47
A Bug's Life - 11/25/98
$162.8M
RT score (critics/audience): 92/61
First Released: Antz
Box Office Winner: A Bug's Life
Better Movie: A Bug's Life
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Deep Impact - 5/8/98
$140.4M
RT score (critics/audience): 47/51
Armageddon - 7/1/98
$201.5M
RT score (critics/audience): 39/77
First Released: Deep Impact
Box Office Winner: Armageddon
Better Movie: Armageddon did worse with critics, but rated higher with audiences. For me - tough call, but I guess I'd go with Armageddon
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Prefontaine - 1/24/97
$589,300
RT score (critics/audience): 59/77
Without Limits - 9/11/98
$777,423
RT score (critics/audience): 79/87
First Released: Prefontaine
Box Office Winner: Without Limits
Better Movie: Without Limits rates higher - I haven't seen either myself
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Dante's Peak - 2/7/97
$67.2M
RT score (critics/audience): 27/45
Volcano - 4/25/97
$47.5M
RT score (critics/audience): 44/43
First Released: Dante's Peak
Box Office Winner: Dante's Peak
Better Movie: another close call, but I'd say Dante's Peak
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Terminal Velocity - 9/23/94
$16.5
RT score (critics/audience): 14/25
Drop Zone - 12/9/94
$28.7M
RT score (critics/audience): 35/38
First Released: Terminal Velocity
Box Office Winner: Drop Zone
Better Movie: Drop Zone
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Tombstone - 12/25/93
$56.5M
RT score (critics/audience): 73/93
Wyatt Earp - 6/24/94
$25.1M
RT score (critics/audience): 42/61
First Released: Tombstone
Box Office Winner: Tombstone
Better Movie: Tombstone has the higher scores. I know most of you will disagree with me, but I prefer Wyatt Earp
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Christopher Columbus: The Discovery - 8/21/92
$8.2M
RT score (critics/audience): 7/18
1492: Conquest of Paradise - 10/9/92
$7.2M
RT score (critics/audience): 39/45
First Released: Christopher Columbus
Box Office Winner: Christopher Columbus
Better Movie: 1492 rates higher - I haven't seen either one

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K-9 - 4/28/89
$43.2M
RT score (critics/audience): 22/45
Turner & Hooch - 7/28/89
$71M
RT score (critics/audience): 62/53
First Released: K-9
Box Office Winner: Turner & Hooch
Better Movie: Turner & Hooch
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Deep Star Six - 1/13/89
$8M
RT score (critics/audience): 0/26
Leviathan - 3/17/89
$15.7M
RT score (critics/audience): 11/30
The Abyss - 8/9/89
$54.2M
RT score (critics/audience): 88/79
First Released: Deep Star Six
Box Office Winner: The Abyss
Better Movie: The Abyss
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Like Father, Like Son - 10/2/87
$34.4M
RT score (critics/audience): NA/36
Vice Versa - 3/11/88
$13.7M
RT score (critics/audience): 43/40
18 Again - 4/8/88
$2.6M
RT score (critics/audience): 29/44
Big - 6/3/88
$115M
RT score (critics/audience): 96/73
First Released: Like Father, Like Son
Box Office Winner: Big
Better Movie: Big
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Iron Eagle - 1/17/86
$24M
RT score (critics/audience): NA/50
Top Gun - 5/16/86
$176M
RT score (critics/audience): 55/80
First Released: Iron Eagle
Box Office Winner: Top Gun
Better Movie: Top Gun