1680x1050 isn't that much these days. Either of your video card choices will let you run games pretty much maxed out.
i5-4670k can be overclocked, so if you aren't planning on it you would be better off with the i5-4590. Either would have more per-core performance then the AMD FX chips, of course, they cost more.
FX chips like the 8320 have 4 dual core modules, effectively eight cores. In applications that can utilize many cores it can perform better then an i5, in general though, for gaming, an i5 is the better choice.
PhysX is a visual modification that some games support, it requires extra processing to handle these visual changes (Things like ragdoll physics and collision). Mantle is more a low-level GPU access language that AMD recently introduced. It allows high levels of optimization at the cost of development time.
Pricing them out comes about the same. With the AMD config you would have better game performance on GPU bound titles, with the intel setup you would do better in CPU bound titles.
Either configuration is a potent gaming machine.
(Personnally I would still add a heatsink to this build, the stock one is merely 'okay')
PCPartPicker part list:
http://pcpartpicker.com/p/dJ2bCJ
Price breakdown by merchant: http://pcpartpicker.com/p/dJ2bCJ/by_merchant/
CPU: Intel Core i5-4590 3.3GHz Quad-Core Processor ($199.98 @ SuperBiiz)
Motherboard: ASRock H97 PRO4 ATX LGA1150 Motherboard ($86.66 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1866 Memory ($76.99 @ Newegg)
Video Card: Asus GeForce GTX 760 2GB DirectCU II Video Card ($216.60 @ Newegg)
Total: $580.23
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-06-13 13:31 EDT-0400
(CPU cooler is almost mandatory, the stock one is quite noisy under load)
PCPartPicker part list:
http://pcpartpicker.com/p/T3MTzy
Price breakdown by merchant: http://pcpartpicker.com/p/T3MTzy/by_merchant/
CPU: AMD FX-8320 3.5GHz 8-Core Processor ($143.99 @ NCIX US)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ OutletPC)
Motherboard: ASRock 970 Extreme3 R2.0 ATX AM3+ Motherboard ($64.99 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1866 Memory ($76.99 @ Newegg)
Video Card: Asus Radeon R9 280X 3GB DirectCU II Video Card ($309.99 @ Newegg)
Total: $625.94
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-06-13 13:33 EDT-0400