For gaming + streaming, the price point would be better for the fx8350. People favor intel over AMD because of intel's single thread performance. I think the i5 might be better now, because of nVidia's shadowplay, but I don't know really. I know with OBS fx8350 does well with it.
Here's a possible build with the fx8350. I feel like I might be missing something.
PCPartPicker part list:
http://pcpartpicker.com/p/2tY1K
Price breakdown by merchant: http://pcpartpicker.com/p/2tY1K/by_merchant/
Benchmarks: http://pcpartpicker.com/p/2tY1K/benchmarks/
CPU: AMD FX-8350 4.0GHz 8-Core Processor ($189.99 @ TigerDirect)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.99 @ Microcenter)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard ($134.98 @ SuperBiiz)
Memory: Team Vulcan 8GB (2 x 4GB) DDR3-1600 Memory ($69.98 @ OutletPC)
Storage: A-Data Premier Pro SP600 64GB 2.5" Solid State Disk ($54.99 @ TigerDirect)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.99 @ NCIX US)
Video Card: MSI GeForce GTX 770 2GB Video Card ($334.98 @ SuperBiiz)
Case: Fractal Design Define R4 (Black Pearl) ATX Mid Tower Case ($88.98 @ Newegg)
Power Supply: Corsair Builder 600W 80+ Bronze Certified ATX Power Supply ($57.99 @ Newegg)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($15.99 @ Microcenter)
Operating System: Microsoft Windows 8.1 - OEM (64-bit) ($94.98 @ OutletPC)
Monitor: Asus VS247H-P 23.6" Monitor ($157.00 @ B&H)
Total: $1289.84
You could also change this build to have an i5 4670k + z87 motherboard. But with a 1500 budget, you could get an i7 + z87 motherboard I'm pretty sure. The I7 would perform better than the 8350 overall when gaming and streaming. This build is with an i7, but you can lower it to an i5 if you would like. You're choice. I'm sure someone could probably improve these builds.
PCPartPicker part list:
http://pcpartpicker.com/p/2tY7q
Price breakdown by merchant: http://pcpartpicker.com/p/2tY7q/by_merchant/
Benchmarks: http://pcpartpicker.com/p/2tY7q/benchmarks/
CPU: Intel Core i7-4770K 3.5GHz Quad-Core Processor ($319.99 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($33.98 @ SuperBiiz)
Motherboard: ASRock Z87 Extreme3 ATX LGA1150 Motherboard ($114.99 @ Microcenter)
Memory: Team Vulcan 8GB (2 x 4GB) DDR3-1600 Memory ($69.98 @ OutletPC)
Storage: A-Data Premier Pro SP600 64GB 2.5" Solid State Disk ($54.99 @ TigerDirect)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.99 @ NCIX US)
Video Card: MSI GeForce GTX 770 2GB Video Card ($334.98 @ SuperBiiz)
Case: Fractal Design Define R4 (Black Pearl) ATX Mid Tower Case ($88.98 @ Newegg)
Power Supply: Corsair Builder 600W 80+ Bronze Certified ATX Power Supply ($57.99 @ Amazon)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($15.99 @ Microcenter)
Operating System: Microsoft Windows 8.1 - OEM (64-bit) ($94.98 @ OutletPC)
Monitor: Asus VS247H-P 23.6" Monitor ($157.00 @ B&H)
Total: $1397.86