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Differences What are the advantages of each

Front view of Radeon HD 8870

Reasons to consider the
AMD Radeon HD 8870

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Significantly better floating-point performance 3,789 GFLOPS vs 1,360 GFLOPS More than 2.8x better floating-point performance
More memory 2,048 MB vs 1,024 MB 2x more memory
Higher clock speed 925 MHz vs 850 MHz Around 10% higher clock speed
Higher memory bandwidth 192 GB/s vs 76.8 GB/s 2.5x higher memory bandwidth
Significantly higher texture rate 118.4 GTexel/s vs 34 GTexel/s Around 3.5x higher texture rate
Higher effective memory clock speed 6,000 MHz vs 4,800 MHz 25% higher effective memory clock speed
Higher pixel rate 29.6 GPixel/s vs 13.6 GPixel/s Around 2.2x higher pixel rate
Significantly more shading units 2,048 vs 800 1248 more shading units
Significantly more texture mapping units 128 vs 40 88 more texture mapping units
Significantly more compute units 32 vs 10 22 more compute units
More render output processors 32 vs 16 Twice as many render output processors
Higher memory clock speed 1,500 MHz vs 1,200 MHz 25% higher memory clock speed
Wider memory bus 256 bit vs 128 bit 2x wider memory bus
Front view of Radeon HD 6770

Reasons to consider the
AMD Radeon HD 6770

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Lower TDP 108W vs 185W More than 40% lower TDP

Features Key features of the Radeon HD 8870  vs 6770 

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

Radeon HD 8870
192 GB/s
Radeon HD 6770
76.8 GB/s
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 8870 | by Tim-Verry (Sep, 2012)

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

Radeon HD 8870
29.6 GPixel/s
Radeon HD 6770
13.6 GPixel/s
The 8850 and 8870 graphics cards are rumored to launch in January 2013 for under $300 and offer up some significant performance and efficiency improvements.
Radeon HD 8870 | by Tim-Verry (Sep, 2012)

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

Radeon HD 8870
118.4 GTexel/s
Radeon HD 6770
34 GTexel/s
The single precision performance has been increased to 2.99 TFLOPS on the 8850 (1.76 TFLOPS on the 7850), and 3.94 TFLOPS on the 8870 (7870 has 2.25 TFLOPS).
Radeon HD 8870 | by Tim-Verry (Sep, 2012)

floating point performance How fast the gpu can crunch numbers

Radeon HD 8870
3,789 GFLOPS
Radeon HD 6770
1,360 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 8870 | by Tim-Verry (Sep, 2012)

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

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 8870 | by Tim-Verry (Sep, 2012)

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

Specifications Full list of technical specs

gpu

Radeon HD 8870  vs
6770 
GPU brand AMD AMD
GPU name Hainan XT Juniper XT
Market Desktop Desktop
Clock speed 925 MHz 850 MHz
Is dual GPU No No
Reference card None None

raw performance

Shading units 2,048 800
Texture mapping units 128 40
Render output processors 32 16
Compute units 32 10
Pixel rate 29.6 GPixel/s 13.6 GPixel/s
Texture rate 118.4 GTexel/s 34 GTexel/s
Floating-point performance 3,789 GFLOPS 1,360 GFLOPS

memory

Radeon HD 8870  vs
6770 
Memory clock speed 1,500 MHz 1,200 MHz
Effective memory clock speed 6,000 MHz 4,800 MHz
Memory bus 256 bit 128 bit
Memory 2,048 MB 1,024 MB
Memory type GDDR5 GDDR5
Memory bandwidth 192 GB/s 76.8 GB/s

noise and power

TDP 185W 108W

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