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Differences What are the advantages of each

Front view of Radeon HD 8750M

Reasons to consider the
AMD Radeon HD 8750M

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Much higher memory bandwidth 64 GB/s vs 12.8 GB/s 5x higher memory bandwidth
Significantly higher effective memory clock speed 4,000 MHz vs 1,600 MHz 2.5x higher effective memory clock speed
Better floating-point performance 476.2 GFLOPS vs 240 GFLOPS Around 2x better floating-point performance
More shading units 384 vs 96 288 more shading units
Higher pixel rate 4.96 GPixel/s vs 2.5 GPixel/s Around 2x higher pixel rate
Wider memory bus 128 bit vs 64 bit 2x wider memory bus
Higher memory clock speed 1,000 MHz vs 800 MHz 25% higher memory clock speed
Slightly more texture mapping units 24 vs 16 8 more texture mapping units
Front view of GeForce 720M

Reasons to consider the
Nvidia GeForce 720M

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GPUBoss is not aware of any important advantages of the Nvidia GeForce 720M vs the AMD Radeon HD 8750M.

Features Key features of the Radeon HD 8750M  vs GeForce 720M 

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

Radeon HD 8750M
64 GB/s
GeForce 720M
12.8 GB/s
With the AMD system only having 4GB of memory compared to the Ivy Bridge system with 8GB, that is one lone "stand out" spec.
Radeon HD 8750M | by Ryan-Shrout (Jun, 2012)

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

Radeon HD 8750M
4.96 GPixel/s
GeForce 720M
2.5 GPixel/s
The Intel HD 4000 graphics offer a noticeable upgrade from the HD 3000 on the Sandy Bridge platform but AMD's new HD 7660G (based on Cayman) also sees performance increase.
Radeon HD 8750M | by Ryan-Shrout (Jun, 2012)

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

Radeon HD 8750M
14.9 GTexel/s
GeForce 720M
10 GTexel/s
We ran our tests at 1366x768 with "high" image quality settings and ran through a section of the early part of the game a few times with FRAPs to get our performance results.
Radeon HD 8750M | by Ryan-Shrout (Jun, 2012)

floating point performance How fast the gpu can crunch numbers

Radeon HD 8750M
476.2 GFLOPS
GeForce 720M
240 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 8750M  vs
GeForce 720M 
GPU brand AMD Nvidia
GPU name Mars GF117
Market Laptop Laptop
Clock speed 620 MHz 625 MHz
Is dual GPU No No
Reference card None None

raw performance

Shading units 384 96
Texture mapping units 24 16
Render output processors 8 8
Pixel rate 4.96 GPixel/s 2.5 GPixel/s
Texture rate 14.9 GTexel/s 10 GTexel/s
Floating-point performance 476.2 GFLOPS 240 GFLOPS

memory

Radeon HD 8750M  vs
GeForce 720M 
Memory clock speed 1,000 MHz 800 MHz
Effective memory clock speed 4,000 MHz 1,600 MHz
Memory bus 128 bit 64 bit
Memory 2,048 MB 2,048 MB
Memory type GDDR5 DDR3
Memory bandwidth 64 GB/s 12.8 GB/s

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