The FX8350 itself is cheaper than the 4570, but you have to pay extra for a decent motherboard for overclocking, and then you have to get an after market cooler too. You could just slap the 4570 in a cheap B85 motherboard and your set. Of course, you don't HAVE to overclock the FX8350, but performance will suffer.
PCPartPicker part list:
http://pcpartpicker.com/p/12i9x
Price breakdown by merchant: http://pcpartpicker.com/p/12i9x/by_merchant/
Benchmarks: http://pcpartpicker.com/p/12i9x/benchmarks/
CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($179.99 @ Amazon)
Motherboard: ASRock B85 Pro4 ATX LGA1150 Motherboard ($69.99 @ Amazon)
Total: $249.98
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-27 14:42 EDT-0400)
PCPartPicker part list:
http://pcpartpicker.com/p/18hEr
Price breakdown by merchant: http://pcpartpicker.com/p/18hEr/by_merchant/
Benchmarks: http://pcpartpicker.com/p/18hEr/benchmarks/
CPU: AMD FX-8350 4.0GHz 8-Core Processor ($189.99 @ Newegg)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ OutletPC)
Motherboard: Gigabyte GA-970A-DS3P ATX AM3+ Motherboard ($64.99 @ Newegg)
Total: $284.96
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-27 14:43 EDT-0400)
It should be noted that even when the FX8350 is heavily overclocked, it still loses out to the 4570 most of the time.