Which is better, a GIGABYTE HD 7870 or a GIGABYTE HD 7770?

I would like to know which one would give me a (generally) better performance in Battlefield 4.
Extra Information
Native Resolution
1920x1080

Links to Cards

http://www.frys.com/product/7382474?site=sr:SEARCH:MAIN_RSLT_PG

http://www.frys.com/product/7382514?site=sr:SEARCH:MAIN_RSLT_PG

DxDiag Info
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System Information
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Time of this report: 12/30/2013, 12:40:13
Machine name: *Censored*
Operating System: Windows 7 Home Premium 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.130828-1532)
Language: English (Regional Setting: English)
System Manufacturer: MSI
System Model: MS-7721
BIOS: BIOS Date: 04/25/13 16:39:35 Ver: 04.06.05
Processor: AMD A10-6800K APU with Radeon(tm) HD Graphics (4 CPUs), ~4.1GHz
Memory: 8192MB RAM
Available OS Memory: 7216MB RAM
Page File: 3239MB used, 11188MB available
Windows Dir: C:\Windows
DirectX Version: DirectX 11
DX Setup Parameters: Not found
User DPI Setting: 96 DPI (100 percent)
System DPI Setting: 96 DPI (100 percent)
DWM DPI Scaling: Disabled
DxDiag Version: 6.01.7601.17514 32bit Unicode

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DxDiag Notes
------------
Display Tab 1: No problems found.
Sound Tab 1: No problems found.
Sound Tab 2: No problems found.
Input Tab: No problems found.

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DirectX Debug Levels
--------------------
Direct3D: 0/4 (retail)
DirectDraw: 0/4 (retail)
DirectInput: 0/5 (retail)
DirectMusic: 0/5 (retail)
DirectPlay: 0/9 (retail)
DirectSound: 0/5 (retail)
DirectShow: 0/6 (retail)

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Display Devices
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Card name: ATI Radeon HD 5700 Series
Manufacturer: Advanced Micro Devices, Inc.
Chip type: AMD Radeon Graphics Processor (0x68BE)
DAC type: Internal DAC(400MHz)
Device Key: Enum\PCI\VEN_1002&DEV_68BE&SUBSYS_57501092&REV_00
Display Memory: 4095 MB
Dedicated Memory: 1014 MB
Shared Memory: 3081 MB
Current Mode: 1920 x 1080 (32 bit) (60Hz)
Monitor Name: Generic PnP Monitor
Monitor Model: ASUS VN247
Monitor Id: ACI24C3
Native Mode: 1920 x 1080(p) (60.000Hz)
Output Type: HDMI
Driver Name: aticfx64.dll,aticfx64.dll,aticfx64.dll,aticfx32,aticfx32,aticfx32,atiumd64.dll,atidxx64.dll,atidxx64.dll,atiumdag,atidxx32,atidxx32,atiumdva,atiumd6a.cap,atitmm64.dll
Driver File Version: 8.17.0010.1242 (English)
Driver Version: 13.200.11.0
DDI Version: 11
Driver Model: WDDM 1.1
Driver Attributes: Final Retail
Driver Date/Size: 9/21/2013 01:45:30, 1287152 bytes
WHQL Logo'd: n/a
WHQL Date Stamp: n/a
Device Identifier: {D7B71EE2-2BFE-11CF-F877-5A77BEC2C535}
Vendor ID: 0x1002
Device ID: 0x68BE
SubSys ID: 0x57501092
Revision ID: 0x0000
Driver Strong Name: oem47.inf:ATI.Mfg.NTamd64.6.1:ati2mtag_Evergreen:13.200.11.0ci\ven_1002&dev_68be
Rank Of Driver: 00E62001
Video Accel: ModeMPEG2_A ModeMPEG2_C
Deinterlace Caps: {6E8329FF-B642-418B-BCF0-BCB6591E255F}: Format(In/Out)=(YUY2,YUY2) Frames(Prev/Fwd/Back)=(0,0,1) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_PixelAdaptive
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{335AA36E-7884-43A4-9C91-7F87FAF3E37E}: Format(In/Out)=(UYVY,UYVY) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_BOBVerticalStretch
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(UYVY,UYVY) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY
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{6E8329FF-B642-418B-BCF0-BCB6591E255F}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,1) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_PixelAdaptive
{335AA36E-7884-43A4-9C91-7F87FAF3E37E}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_BOBVerticalStretch
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(IMC1,UNKNOWN) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
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D3D9 Overlay: Not Supported
DXVA-HD: Not Supported
DDraw Status: Enabled
D3D Status: Enabled
AGP Status: Enabled