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Differences What are the advantages of each

Front view of Radeon HD 7670

Reasons to consider the
AMD Radeon HD 7670

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Lower TDP 66W vs 151W 2.3x lower TDP
Front view of Radeon HD 6870

Reasons to consider the
MSI Radeon HD 6870

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Higher clock speed 930 MHz vs 800 MHz More than 15% higher clock speed
Significantly higher pixel rate 29.8 GPixel/s vs 6.4 GPixel/s Around 4.8x higher pixel rate
Better floating-point performance 2,083 GFLOPS vs 768 GFLOPS Around 2.8x better floating-point performance
Higher memory bandwidth 134.4 GB/s vs 64 GB/s More than 2x higher memory bandwidth
Significantly more render output processors 32 vs 8 24 more render output processors
Higher texture rate 52.1 GTexel/s vs 19.2 GTexel/s Around 2.8x higher texture rate
More shading units 1,120 vs 480 640 more shading units
More texture mapping units 56 vs 24 32 more texture mapping units
Wider memory bus 256 bit vs 128 bit 2x wider memory bus
More compute units 14 vs 6 8 more compute units

Features Key features of the Radeon HD 7670  vs 6870 

memory bandwidth Rate at which data can be read from or stored in onboard memory

Radeon HD 7670
64 GB/s
Radeon HD 6870
134.4 GB/s
An additional cooling plate is installed to cool the memory and voltage regulation circuitry.
Radeon HD 6870 | by techPowerUp! (Oct, 2010)

pixel rate Number of pixels a graphics card can render to the screen every second

Radeon HD 7670
6.4 GPixel/s
Radeon HD 6870
29.8 GPixel/s
Thanks to the higher clocks out of the box it has a 3% performance advantage over reference design HD 6870's which is decent but not spectacular.
Radeon HD 6870 | by techPowerUp! (Feb, 2011)

texture rate Speed at which a graphics card can perform texture mapping

Radeon HD 7670
19.2 GTexel/s
Radeon HD 6870
52.1 GTexel/s
But then, it is the maximum configuration of the HD 6870, you cannot add a third of fourth card later, if you need more performance.
Radeon HD 6870 | by techPowerUp! (Oct, 2010)

floating point performance How fast the gpu can crunch numbers

Radeon HD 7670
768 GFLOPS
Radeon HD 6870
2,083 GFLOPS

shading units Subcomponents of the gpu, these run in parallel to enable fast pixel shading

texture mapping units Built into each gpu, these resize and rotate bitmaps for texturing scenes

Specifications Full list of technical specs

gpu

Radeon HD 7670  vs
6870 
GPU brand AMD AMD
GPU name Turks XT Barts XT
Market Desktop Desktop
Clock speed 800 MHz 930 MHz
Is dual GPU No No
Reference card AMD Radeon HD 7670 OEM 800 MHz 512 MB AMD Radeon HD 6870 900 MHz 1 GB

raw performance

Shading units 480 1,120
Texture mapping units 24 56
Render output processors 8 32
Compute units 6 14
Pixel rate 6.4 GPixel/s 29.8 GPixel/s
Texture rate 19.2 GTexel/s 52.1 GTexel/s
Floating-point performance 768 GFLOPS 2,083 GFLOPS

memory

Radeon HD 7670  vs
6870 
Memory clock speed 1,000 MHz 1,050 MHz
Effective memory clock speed 4,000 MHz 4,200 MHz
Memory bus 128 bit 256 bit
Memory 1,024 MB 1,024 MB
Memory type GDDR5 GDDR5
Memory bandwidth 64 GB/s 134.4 GB/s

noise and power

TDP 66W 151W

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