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Differences What are the advantages of each

Front view of Radeon HD 5870 Eyefinity 6

Reasons to consider the
ATi Radeon HD 5870 Eyefinity 6

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Slightly higher clock speed 850 MHz vs 836 MHz Almost the same
Slightly lower TDP 228W vs 250W Around 10% lower TDP
Front view of GeForce GTX TITAN

Reasons to consider the
Nvidia GeForce GTX TITAN

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Much more memory 6,144 MB vs 2,048 MB 3x more memory
Significantly higher texture rate 187.3 GTexel/s vs 68 GTexel/s More than 2.8x higher texture rate
Higher memory bandwidth 288.4 GB/s vs 153.6 GB/s Around 90% higher memory bandwidth
Better floating-point performance 4,494 GFLOPS vs 2,720 GFLOPS More than 65% better floating-point performance
Higher effective memory clock speed 6,008 MHz vs 4,800 MHz More than 25% higher effective memory clock speed
Significantly more texture mapping units 224 vs 80 144 more texture mapping units
Higher pixel rate 46.8 GPixel/s vs 27.2 GPixel/s More than 70% higher pixel rate
More shading units 2,688 vs 1,600 1088 more shading units
More render output processors 48 vs 32 16 more render output processors
Higher memory clock speed 1,502 MHz vs 1,200 MHz More than 25% higher memory clock speed
Wider memory bus 384 bit vs 256 bit 50% wider memory bus

Features Key features of the Radeon HD 5870 Eyefinity 6  vs GeForce GTX TITAN 

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

Don't get too excited as we're looking at a comparison of GFLOPS and not game performance, but the peak theoretical ALU bound performance of mobile Kepler should exceed that of a Playstation 3 or GeForce 8800 GTX (memory bandwidth is another story however).
Radeon HD 5870 Eyefinity 6 | by Anand-Lal-Shimpi (Jul, 2013)

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

GeForce GTX TITAN
46.8 GPixel/s
Sniper Elite V2 performance is just massive across the board with strong gains and fantastic overall numbers for anyone wanting some serious FPS for solid gameplay.
Radeon HD 5870 Eyefinity 6 | by Shawn-Baker (Apr, 2013)

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

GeForce GTX TITAN
187.3 GTexel/s
Heaven performance is very impressive with some truly excellent gains being seen.
Radeon HD 5870 Eyefinity 6 | by Shawn-Baker (Apr, 2013)

floating point performance How fast the gpu can crunch numbers

GeForce GTX TITAN
4,494 GFLOPS
To hit 400 GFLOPS you'd need to clock the mobile Kepler GPU at roughly 1GHz.
Radeon HD 5870 Eyefinity 6 | by Anand-Lal-Shimpi (Jul, 2013)

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

These are the first drivers to support OpenGL 4.3, which among other things means this is the first GeForce driver set to have support for new features such as OpenGL compute shaders, along with full OpenGL ES 3.0 superset functionality.
Radeon HD 5870 Eyefinity 6 | by Ryan-Smith (Oct, 2012)

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

From a technical perspective, the GeForce GTX 980 HOF will feature 2048 CUDA Cores, 128 TMUs, 64 ROPs and a 4 GB GDDR5 VRAM running across a 256-bit bus interface.
Radeon HD 5870 Eyefinity 6 | by hassan-mujtaba (Sep, 2014)

Specifications Full list of technical specs

gpu

Radeon HD 5870 Eyefinity 6  vs
GeForce GTX TITAN 
GPU brand ATi Nvidia
GPU name Cypress GK110
Market Desktop Desktop
Clock speed 850 MHz 836 MHz
Is dual GPU No No
Reference card None None

raw performance

Shading units 1,600 2,688
Texture mapping units 80 224
Render output processors 32 48
Pixel rate 27.2 GPixel/s 46.8 GPixel/s
Texture rate 68 GTexel/s 187.3 GTexel/s
Floating-point performance 2,720 GFLOPS 4,494 GFLOPS

memory

Radeon HD 5870 Eyefinity 6  vs
GeForce GTX TITAN 
Memory clock speed 1,200 MHz 1,502 MHz
Effective memory clock speed 4,800 MHz 6,008 MHz
Memory bus 256 bit 384 bit
Memory 2,048 MB 6,144 MB
Memory type GDDR5 GDDR5
Memory bandwidth 153.6 GB/s 288.4 GB/s

noise and power

TDP 228W 250W

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