If intel is relly that much better how about the i5 2500 or 2600
Those are older gens, and therefor slower.
Intel has been ahead of AMD for a while. You can look at core count and GHz speed all day long, but that doesn't tell you the full story on performance. There is much to be gained from technological improvements outside of those two markers.
Your proposed CPU vs what I suggested:
http://cpuboss.com/cpus/Intel-Pentium-G4400-vs-AMD-Athlon-X4-860K
For gaming performance, you definitely want multi-core, but there comes a point where single core performance is more impactful than having more cores.
As to i3/i5 etc, it simply does not fit the budget you have laid out.
The system I posted above fits your budget, and leaves you with a working component in every aspect. Then, simply throw bolts ons in along the way (the first being the SSD IMO). The other thing is that you'd be spending $65 on a CPU with fairly good performance, that could easily be replaced later by something with REALLY good performance:
http://cpuboss.com/cpus/Intel-Pentium-G4400-vs-Intel-Core-i5-6600
The single core performance is just slightly in favor of the i5, so your biggest improvements would be from games hitting more than 2 cores.
If all I had was $400, I'd likely go the route I posted as it puts you on the latest Intel platform with an easy upgrade path.
Now, if you throw more $$$$ at your build, you can bump a good number of things in the right direction.
Lastly, if your Win7 tag is legit and you can get it activated, you should be able to upgrade to Win10 for free still. With that money, I'd likely look at a better GPU, and upgrade to an SSD in the future... actually, you could just about squeeze one in the SSD with an extra 20/30:
PCPartPicker part list:
http://pcpartpicker.com/p/PZz9sY
Price breakdown by merchant:
http://pcpartpicker.com/p/PZz9sY/by_merchant/
CPU: Intel Pentium G4400 3.3GHz Dual-Core Processor ($64.28 @ Amazon)
Motherboard: Gigabyte GA-H110M-A Micro ATX LGA1151 Motherboard ($37.98 @ Newegg)
Memory: Crucial Ballistix Sport LT 8GB (1 x 8GB) DDR4-2400 Memory ($31.99 @ Amazon)
Storage: Crucial BX200 240GB 2.5" Solid State Drive ($64.99 @ Amazon)
Video Card: EVGA GeForce GTX 950 2GB SSC ACX 2.0 Video Card ($163.98 @ Newegg)
Case: Fractal Design Core 1000 USB 3.0 MicroATX Mid Tower Case ($29.99 @ Newegg)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($35.98 @ Newegg)
Total: $429.19
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-03-03 09:39 EST-0500