Which build for streaming/recording games

Build 2 is better. One quick question do you want to overclock? If you do not overclock I can get you a better build for the same price and double the virtual cores on the i5.

Build 2 has a better CPU. It also has a excellent mobo and rest of parts.

I will also say the build needs 1 improvement especially that is the PSU. Corsair builder PSU's are notoriously bad and not recommended for gaming systems like this. You do not want to risk your other parts for a 20 dollar benefit.

Even better build for steaming and gaming for not much more. This build is equal power to an i7 just without the overclocking ability.
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Xeon E3-1231 V3 3.4GHz Quad-Core Processor ($242.99 @ SuperBiiz)
Motherboard: Gigabyte GA-H97-D3H ATX LGA1150 Motherboard ($86.99 @ SuperBiiz)
Memory: G.Skill Ripjaws X Series 16GB (2 x 8GB) DDR3-1600 Memory ($89.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($46.89 @ OutletPC)
Video Card: MSI GeForce GTX 970 4GB Twin Frozr V Video Card ($339.99 @ SuperBiiz)
Case: Thermaltake Commander MS-I ID ATX Mid Tower Case ($32.99 @ Micro Center)
Power Supply: EVGA SuperNOVA GS 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($65.98 @ Newegg)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($14.98 @ OutletPC)
Operating System: Microsoft Windows 8.1 OEM (64-bit) ($86.98 @ OutletPC)
Wireless Network Adapter: Asus PCE-N53 802.11a/b/g/n PCI-Express x1 Wi-Fi Adapter ($10.31 @ Newegg)
Monitor: Acer G226HQLBbd 60Hz 21.5" Monitor ($89.99 @ Newegg)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($27.99 @ Amazon)
Total: $1136.07
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-07-06 10:52 EDT-0400
 
More than both the i5 and AMD. Probably 10+% more for 6 dollars more if you stream / render. If you do not overclock it is a no brainer to get the Xeon :)

Also the 6 dollars is well made up with the better quality PSU.
If you want you can change the mobo I selected with the Gaming 5 Gigabyte as it is a very good mobo and will allow for SLI and it has a better color scheme.
 
The build you posted only has a 6 dollar difference but I will see what I can do to make build 2 have a Xeon.
You realistically only need 8GB of RAM to start with you can always upgrade it later. Made the mobo cheaper. Still about 27 dollars off but well worth it.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Xeon E3-1231 V3 3.4GHz Quad-Core Processor ($242.99 @ SuperBiiz)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard ($69.89 @ OutletPC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($48.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($46.89 @ OutletPC)
Video Card: MSI GeForce GTX 970 4GB Twin Frozr V Video Card ($339.99 @ SuperBiiz)
Case: Thermaltake Commander MS-I ID ATX Mid Tower Case ($32.99 @ Micro Center)
Power Supply: EVGA SuperNOVA GS 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($65.98 @ Newegg)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($14.98 @ OutletPC)
Operating System: Microsoft Windows 8.1 OEM (64-bit) ($86.98 @ OutletPC)
Wireless Network Adapter: Asus PCE-N53 802.11a/b/g/n PCI-Express x1 Wi-Fi Adapter ($10.31 @ Newegg)
Monitor: Acer G226HQLBbd 60Hz 21.5" Monitor ($89.99 @ Newegg)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($27.99 @ Amazon)
Total: $1077.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-07-06 11:17 EDT-0400
 
Your very welcome :)
If you have more questions you can post again or send me a PM.

Also if you want you can save another 10 dollars to change to an EVGA Superclocked card as they are really good :)

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Xeon E3-1231 V3 3.4GHz Quad-Core Processor ($242.99 @ SuperBiiz)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard ($69.89 @ OutletPC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($48.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($46.89 @ OutletPC)
Video Card: EVGA GeForce GTX 970 4GB Superclocked ACX 2.0 Video Card ($329.99 @ Amazon)
Case: Thermaltake Commander MS-I ID ATX Mid Tower Case ($32.99 @ Micro Center)
Power Supply: EVGA SuperNOVA GS 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($65.98 @ Newegg)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($14.98 @ OutletPC)
Operating System: Microsoft Windows 8.1 OEM (64-bit) ($86.98 @ OutletPC)
Wireless Network Adapter: Asus PCE-N53 802.11a/b/g/n PCI-Express x1 Wi-Fi Adapter ($10.31 @ Newegg)
Monitor: Acer G226HQLBbd 60Hz 21.5" Monitor ($89.99 @ Newegg)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($27.99 @ Amazon)
Total: $1067.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-07-06 11:23 EDT-0400