AMD is definitely cheaper, but lacks the performance of Intel. I would go Intel.
Moderate price build below:
PCPartPicker part list:
http://pcpartpicker.com/p/X874Bm
Price breakdown by merchant: http://pcpartpicker.com/p/X874Bm/by_merchant/
CPU: Intel Core i7-4790K 4.0GHz Quad-Core Processor ($318.99 @ SuperBiiz)
Motherboard: Asus Z97-A ATX LGA1150 Motherboard ($139.99 @ SuperBiiz)
Total: $458.98
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-05-16 12:45 EDT-0400
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High price but best performance build below:
PCPartPicker part list:
http://pcpartpicker.com/p/B43fLk
Price breakdown by merchant: http://pcpartpicker.com/p/B43fLk/by_merchant/
CPU: Intel Core i7-6700K 4.0GHz Quad-Core Processor ($343.99 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.89 @ OutletPC)
Motherboard: MSI Z170A GAMING M5 ATX LGA1151 Motherboard ($156.98 @ Newegg)
Total: $525.86
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-05-16 12:46 EDT-0400
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Cheap moderate performance build below:
PCPartPicker part list:
http://pcpartpicker.com/p/WwnHxr
Price breakdown by merchant: http://pcpartpicker.com/p/WwnHxr/by_merchant/
CPU: AMD FX-8350 4.0GHz 8-Core Processor ($149.95 @ Amazon)
Motherboard: Asus M5A99FX PRO R2.0 ATX AM3+ Motherboard ($118.99 @ Amazon)
Total: $268.94
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-05-16 12:48 EDT-0400
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Cheapest but low performance build below:
PCPartPicker part list:
http://pcpartpicker.com/p/Z8TBmG
Price breakdown by merchant: http://pcpartpicker.com/p/Z8TBmG/by_merchant/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($98.95 @ Amazon)
Motherboard: Gigabyte GA-78LMT-USB3 Micro ATX AM3+ Motherboard ($46.98 @ Newegg)
Total: $145.93
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-05-16 12:48 EDT-0400
The general difference between Intel and AMD is that Intel focuses more on single threaded performance while AMD tends to focus more on the total amount of cores. So if you want gaming performance, you need to consider that most games will not use all available cores and therefore will play better on Intel.