The 1600 comes with a better Wraith Spire cooler included, and you can OC it to faster clock speeds. Ryzen shines with higher frequency RAM.
List below is $15 more with better cpu, ram and psu. This build will last you much longer than your original one.
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor ($218.55 @ OutletPC)
Motherboard: MSI - B350 TOMAHAWK ATX AM4 Motherboard ($107.99 @ SuperBiiz)
Memory: Team - T-Force / Night Hawk 16GB (2 x 8GB) DDR4-3000 Memory ($104.99 @ Newegg)
Storage: Kingston - HyperX Fury 240GB 2.5" Solid State Drive ($80.99 @ Amazon)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($47.45 @ OutletPC)
Video Card: Gigabyte - Radeon RX 580 4GB Gaming 4G Video Card ($188.99 @ SuperBiiz)
Case: NZXT - S340 (White) ATX Mid Tower Case ($64.99 @ Amazon)
Power Supply: SeaSonic - S12II 520W 80+ Bronze Certified ATX Power Supply ($44.89 @ Newegg)
Total: $858.84
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-06 23:43 EDT-0400