Can this build be improved? $600 Gaming Build

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4170 3.7GHz Dual-Core Processor ($107.99 @ NCIX US)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($45.98 @ OutletPC)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-2400 Memory ($29.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($45.88 @ OutletPC)
Video Card: PowerColor Radeon R9 380 4GB PCS+ Video Card ($179.99 @ Newegg)
Case: Corsair SPEC-01 RED ATX Mid Tower Case ($34.99 @ Micro Center)
Power Supply: XFX TS 550W 80+ Bronze Certified ATX Power Supply
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($15.99 @ Newegg)
Operating System: Microsoft Windows 10 Home OEM (64-bit) ($89.88 @ OutletPC)
Total: $550.69
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-12-28 02:38 EST-0500

With I3,your card will perform better.

BO 3 med-high settings 1080p 60+
BF4 high settings 1080p 60+
 
http://pcpartpicker.com/p/89x9Vn

That's roughly what I'd get; I don't have time to refine that further. Sure it's "only" a dual-core with HT but check the benchmarks.

*Having said that, the two titles you list are well threaded so the FX-6300 should do well or possibly even beat the i3-4170 by a small amount. I'd be surprised if it did though.

For other titles you can lose a lot of performance.

The i3-4170 vs stock FX-6300 is about 50% more powerful per core (not counting hyperthreading).

If we assume Passmark is roughly accurate the FX-6300 must be over 80% load to break even (higher load benefits the FX-6300, but lower means the i3-4170 wins). So that's about 25% faster if both processors are at 100% load which is pretty rare for gaming (never?).
 


Your build is FINE, I was recommended that athlon, just overclock it and use a Cooler Master hyper 212 EVO, but if you are given the option to upgrade for a good price, go for it.

 


Time for some math . Assuming the i3 is around 50% more powerful per core [ and that is a ballpark figure] then the strengths of the two cpus can be summarized as

FX 6300 = 100 +100+ 100 +100 + 100 +100 = 600
i3-4170 = 150 + 150 = 300
Hyperthreading will not improve the i3 in that comparison . All it does is help fully use a core by running two threads at the same time .
The FX will lose some ground because cores do not scale perfectly in practical software usage .
But it does show that the FX is potentially much more powerful when software can make use of the cores.
Its also hard to measure per core performance in the real world . There is very little software than is only singlethreaded so that situation has to be artificially created for "benchmarks"

Things that do increase load on a cpu are high player counts in game maps . Typically in online games that can use the available cores, you can expect the FX to easily out perform the i3 .
In single player that is reversed with the i3 scoring marginal wins in most situations . Overclocking the FX to 4.2 Ghz then swings performance back in the FX's favor
 
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($129.89 @ OutletPC)
CPU Cooler: RAIJINTEK AIDOS 48.6 CFM Sleeve Bearing CPU Cooler ($25.85 @ Amazon)
Motherboard: ASRock Z170M Pro4S Micro ATX LGA1151 Motherboard ($98.99 @ SuperBiiz)
Memory: G.Skill Ripjaws 4 series 8GB (2 x 4GB) DDR4-2400 Memory ($39.99 @ Newegg)
Storage: Hitachi Ultrastar 1TB 3.5" 7200RPM Internal Hard Drive ($41.95 @ Amazon)
Video Card: Gigabyte Radeon R9 380 2GB Video Card ($174.99 @ NCIX US)
Case: Rosewill Galaxy-02 ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($39.99 @ Amazon)
Total: $591.64
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-12-28 15:55 EST-0500

this can be overclocked EASILY to 4.7 GHz, where it performs similar to the i5.

http://www.techspot.com/review/1108-intel-locked-skylake-cpu-bclk-overclocking/
 
Solution
Sqrl is right bout the intel build . If you are going to commit to an i3 at least make it a skylake one .
Since you have the m-ATX motherboard you might as well have an m-ATX case for a smaller more compact computer

The faster RAM is going to be more forgiving with a BLCK overclock since its speeds will rise along with processor speed . The simplest thing to do is set it to 2400 Mhz and then OC . It will not be running too fast after you have OCed the processor

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($129.89 @ OutletPC)
CPU Cooler: RAIJINTEK AIDOS 48.6 CFM Sleeve Bearing CPU Cooler ($25.85 @ Amazon)
Motherboard: ASRock Z170M Pro4S Micro ATX LGA1151 Motherboard ($98.99 @ SuperBiiz)
Memory: G.Skill Ripjaws 4 Series 8GB (2 x 4GB) DDR4-2800 Memory ($46.99 @ Newegg)
Storage: Hitachi Ultrastar 1TB 3.5" 7200RPM Internal Hard Drive ($41.95 @ Amazon)
Video Card: Gigabyte Radeon R9 380 2GB Video Card ($174.99 @ NCIX US)
Case: Fractal Design Core 1000 USB 3.0 MicroATX Mid Tower Case ($34.99 @ Micro Center)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($34.99 @ NCIX US)
Total: $588.64
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-12-28 16:18 EST-0500