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Differences What are the advantages of each

Front view of Radeon HD 8850

Reasons to consider the
AMD Radeon HD 8850

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Significantly higher clock speed 1,000 MHz vs 800 MHz 25% higher clock speed
Significantly better floating-point performance 3,072 GFLOPS vs 768 GFLOPS 4x better floating-point performance
Significantly higher pixel rate 32 GPixel/s vs 6.4 GPixel/s 5x higher pixel rate
Significantly higher texture rate 96 GTexel/s vs 19.2 GTexel/s 5x higher texture rate
More memory 2,048 MB vs 1,024 MB 2x more memory
Higher memory bandwidth 153.6 GB/s vs 64 GB/s Around 2.5x higher memory bandwidth
Higher effective memory clock speed 4,800 MHz vs 4,000 MHz 20% higher effective memory clock speed
Significantly more render output processors 32 vs 8 24 more render output processors
More shading units 1,536 vs 480 1056 more shading units
More texture mapping units 96 vs 24 72 more texture mapping units
More compute units 24 vs 6 18 more compute units
Wider memory bus 256 bit vs 128 bit 2x wider memory bus
Higher memory clock speed 1,200 MHz vs 1,000 MHz 20% higher memory clock speed
Front view of Radeon HD 6670

Reasons to consider the
AMD Radeon HD 6670

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Lower TDP 66W vs 150W 2.3x lower TDP

Features Key features of the Radeon HD 8850  vs 6670 

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

Radeon HD 8850
153.6 GB/s
Radeon HD 6670
64 GB/s
Both overclocks are nice, especially the GDDR5 memory with its high-clock potential can help a lot.
Radeon HD 6670 | by techPowerUp! (Apr, 2011)

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

Radeon HD 8850
32 GPixel/s
Radeon HD 6670
6.4 GPixel/s
In this performance segment DirectX 11 support really doesn't offer much of a benefit, instead of improving performance by using the new API, all developers use it to add eye candy which reduces performance even more.
Radeon HD 6670 | by techPowerUp! (Apr, 2011)

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

Radeon HD 8850
96 GTexel/s
Radeon HD 6670
19.2 GTexel/s
For just $10 more you can get a HD 5750 and $20 more gets you a HD 5770, both of which offer more performance.
Radeon HD 6670 | by techPowerUp! (Apr, 2011)

floating point performance How fast the gpu can crunch numbers

Radeon HD 8850
3,072 GFLOPS
Radeon HD 6670
768 GFLOPS
The figures are not really suited/representative of high performance computing (HPC) workloads where precision is important (think simulations and high-end mathematics), and that is where the double precision numbers come in.
Radeon HD 8850 | by Tim-Verry (Sep, 2012)

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

So while the memory bus and number of ROP units is staying the same, you are getting more shaders and texture units along with a boost to the overall memory bandwidth with the larger die size – sounds like an okay compromise to me!
Radeon HD 8850 | by Tim-Verry (Sep, 2012)

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

The 8850 graphics card will scale the Oland GPU down a bit further by featuring only 1536 shader units and 96 TMUs, but keeping the 32 ROPs and 256-bit interface.
Radeon HD 8850 | by Tim-Verry (Sep, 2012)

Specifications Full list of technical specs

gpu

Radeon HD 8850  vs
6670 
GPU brand AMD AMD
GPU name Hainan PRO Turks XT
Market Desktop Desktop
Clock speed 1,000 MHz 800 MHz
Is dual GPU No No
Reference card None None

raw performance

Shading units 1,536 480
Texture mapping units 96 24
Render output processors 32 8
Compute units 24 6
Pixel rate 32 GPixel/s 6.4 GPixel/s
Texture rate 96 GTexel/s 19.2 GTexel/s
Floating-point performance 3,072 GFLOPS 768 GFLOPS

memory

Radeon HD 8850  vs
6670 
Memory clock speed 1,200 MHz 1,000 MHz
Effective memory clock speed 4,800 MHz 4,000 MHz
Memory bus 256 bit 128 bit
Memory 2,048 MB 1,024 MB
Memory type GDDR5 GDDR5
Memory bandwidth 153.6 GB/s 64 GB/s

noise and power

TDP 150W 66W

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