Most of the Streamers are getting sponsored by Intel, so no real coincidence there. For Gaming and Streaming at the same time the 1600 in my opinion is just as good as the Intel i5-8400.
For me the Ryzen 5 1600 with the 1080 is the way to go, because you can easily overclock the 1600 to atleast 3.9 GhZ.
AMD Build:
PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor (£175.19 @ Aria PC) CPU Cooler: be quiet! - Dark Rock Pro 3 67.8 CFM Fluid Dynamic Bearing CPU Cooler (£50.38 @ Amazon UK) Motherboard: MSI - X370 GAMING PRO CARBON ATX AM4 Motherboard (£129.99 @ Amazon UK) Memory: G.Skill - Ripjaws 4 Series 16GB (2 x 8GB) DDR4-3000 Memory (£135.51 @ Amazon UK) Video Card: Asus - GeForce GTX 1080 8GB TURBO Video Card (£468.99 @ Ebuyer) Power Supply: EVGA - SuperNOVA G2 650W 80+ Gold Certified Fully-Modular ATX Power Supply (£86.44 @ Amazon UK) Total: £1046.50 Prices include shipping, taxes, and discounts when available Generated by PCPartPicker 2017-11-15 22:36 GMT+0000