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Differences What are the advantages of each

Front view of Radeon X1050

Reasons to consider the
ATi Radeon X1050

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Slightly more render output processors 8 vs 4 Twice as many render output processors
Front view of Radeon HD 5450 Passive

Reasons to consider the
ATi Radeon HD 5450 Passive

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Much higher clock speed 650 MHz vs 400 MHz Around 65% higher clock speed
Slightly higher effective memory clock speed 800 MHz vs 400 MHz 2x higher effective memory clock speed
Higher memory clock speed 400 MHz vs 200 MHz 2x higher memory clock speed

Benchmarks Real world tests of Radeon X1050 vs HD 5450 Passive

Passmark Industry standard benchmark for overall graphics card performance

Features Key features of the Radeon X1050  vs HD 5450 Passive 

effective memory clock speed Frequency at which memory can be read from and written to

The memory would feature a clock speed of 3500 MHz while the core would be clocked a little lower than the 1 GHz mark.
Radeon X1050 | by hassan-mujtaba (Sep, 2013)

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

In either case, the Hawaii GPU would feature a 384-bit memory buffer with possibly 3-6 GB of memory.
Radeon X1050 | by hassan-mujtaba (Sep, 2013)

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

Radeon X1050
3.2 GPixel/s
Radeon HD 5450 Passive
2.6 GPixel/s
On desktop systems, driver overhead can decrease frame rate, while on mobile devices driver overhead is more insidious-robbing both battery life and frame rate.
Radeon X1050 | by Ryan-Shrout (Feb, 2014)

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

Radeon X1050
3.2 GTexel/s
Radeon HD 5450 Passive
5.2 GTexel/s
The system, three Radeon HD 7970s in Crossfire, successfully drove... they were playing Dirt 3, by the way... the three monitors at 60 Hz with between 62 and 70, of software recorded, FPS.
Radeon X1050 | by Scott-Michaud (Jul, 2013)

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

3DCenter has built up two assumptions regarding the Hawaii GPU, in the first case scenario the Hawaii GPU would end up with 44 Compute Units which would amount to 2816 stream processors , 176 TMUs, 32-48 ROPs while in the second scenario which seems much more possible, the Hawaii GPU would feature 40 Compute Units which would amount to 2560 stream processors, 160 TMUs, 32-48 ROPs.
Radeon X1050 | by hassan-mujtaba (Sep, 2013)

render output processors GPU commponents responsible for transform pixels as they flow between memory buffers

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