XBOX ONE and PS4 are about the same power, and here's why:
PS4 has 8GB GDDR5 RAM which is very high bandwidth but very high latency. On the other hand, XBOX ONE has 8GB DDR3 RAM which is moderate bandwidth but very low latency, and XBOX ONE also has 32MB of ESRAM which is extremely efficient with very high bandwidth. ESRAM allows for easier access to the entire pipeline of memory bandwidth. This makes the difference between memory on the two consoles a wash. In other words, it's unlikely there will be much performance difference between the two.
For a history lesson: The XBOX 360 didn't only use GDDR3 RAM. It's GPU also had fast 10MB EDRAM connected to it. This EDRAM gave the XBOX 360 higher graphics memory bandwidth than the PS3 and this often showed in multiplat games which had better graphics and framerates on the XBOX 360.
Just throwing expensive memory (GDDR5, in this case) into a console doesn't necessarily make it better. The engineering counts for a lot too, and I would assume that Microsoft's research and development teams are probably fair bit more talented than Sony's research and development teams. However, Sony does make good electronics also.
In addition, the GPU differences between the XBOX ONE and PS4 are not enough to be noticeable in real-world gameplay and heres why: For example, take a gaming PC, stick a AMD Radeon 7790 GPU in it, and play a game. Then take the 7790 out, stick a AMD Radeon 7870 GPU in it, and play the same game. The difference will hardly be noticeable. You might see a few frames per second difference (not noticeable once you are at 30 FPS or more) or be able to play the game at a tiny bit higher graphics setting (hardly noticeable at all). When comparing similar strength same-generation GPUs, it's not until you get into stuff like multiple GPU setups (Crossfire/SLI) that the difference really shows (if the game supports Crossfire/SLI).
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