APU: AMD A10-5800k trinity 3.8 quad core with radeon HD 7660D (intergrated)- 130$
Ram (8gb)-50$
Case w/PSU:rosewill mid tower case with PSU-60$
Motherboard- 50$
HDD- 1tb- 100$
Case fan: 5-10$
monitor- use old one
total= 390 tax not included

ps4 requires +50$ for online and since pc is free this is a good build

That adds up to $400.00 without tax actually.  The RAM price is waaaaaaaay off, you are using DDR3 RAM in your build, where-as the PS4 is using GDDR5 which is much better, but much more expensive...Several hundred dollars expensive.  

Also you forgot to include the price of the OS which will run you about $100.

To build a PC like a PS4 is COMPLETELY impossible due to the way the PS4 is built. 

People underestimate exactly what the PS4 is cabable of.

1.) It has absoltutely ZERO bottleneck issues which is generally impossible for PC's because PC parts arent made specifically to work with certain parts.  The parts in the PS4 are all built specifically to work around each other. 

2.) Yo cannot buy the majority of what you will find in the PS4 as nearly everything is custom built.  Hell even GDDR5 RAM being used as System RAM was truly unheard of until the PS4 was announced.

The point is, the PS4 is several times better than any PC you could build with similar specs, and also cheaper. 

You are aware, of course, that A10 + 6670/7670 combo will perform at best at level of 6770/7750, and that even vanilla 7850 (let alone PS4's GPU) performs at 2x 7750?

It was unheard of because it's not very well suited for general purpose computing.  Latency is way too high.  

By the way, it's not "several hundred dollars more expensive" either.  Yes, it cost more because it's not developed in the same bulk rate capacity as DDR3.  Actually, I take that back, it is developed at the same bulk rate capacity because GDDR5 IS DDR3...just with some tweaks to the timings to allow greater bandwidth and more I/O busses.

Bottlenecks become less of an issue with PC's. They also use GDDR5 for Vram. The main problem with a PC now is with consoles having so much you will see current video cards with 2GB of Vram start to struggle.

HD 6670 - 768 GFLOPS
HD 7660D - 614 GFLOPS

Total - 1,382 GFLOPS.  That's much more than the HD 7750 but equal to a single HD 6770

Or if the APU will let you crossfire with an HD 6770 for $30 extra, there's your more than equal performance (614 + 1360 = 1,974 GFLOPS).

Yes, and its not even close to being on par with PS4.

yes, an awesome one with a gtx670, i5 3570k and 16GB ram

Oh boy, here we go again with FLOPSing....

6770 is rebranded 5770 http://www.rage3d.com/articles/amd_radeon_hd6770-6750_rebranding/

and this is how it compares to 7750:

http://www.anandtech.com/bench/Product/538?vs=535

Now, 7850 vs 7750:

http://www.anandtech.com/bench/Product/549?vs=535

and 7850 vs 5770:

http://www.anandtech.com/bench/Product/549?vs=538

Pretty much identical to mine so :) Not taking anything else into account.

But you can buy a pc that compares with the PS4 for 400-450.