What to upgrade from 3 year old budget build?

I made a budget build for my brother about 3 years ago, but now I see that he struggles to play games. He set his resolution to 720p for overwatch and still averages about 25-35fps.This is his build:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD - Athlon X4 750K 3.4GHz Quad-Core Processor
Motherboard: MSI - FM2-A75MA-E35 Micro ATX FM2 Motherboard
Memory: Team - Vulcan 8GB (2 x 4GB) DDR3-2133 Memory ($59.99)
Storage: Seagate - Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($58.89 @ OutletPC)
Video Card: PowerColor - Radeon HD 7750 1GB Video Card
Case: Antec - VSK-3000 MicroATX Mid Tower Case
Power Supply: Corsair - CX 430W 80+ Bronze Certified Semi-Modular ATX Power Supply ($78.88 @ OutletPC)
Wireless Network Adapter: Rosewill - RNX-N250PCe PCI-Express x1 802.11b/g/n Wi-Fi Adapter ($15.89 @ OutletPC)
Total: $213.65
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-06-21 17:23 EDT-0400

He plays games such as overwatch, HoTS, League of Legends, etc. I feel like upgrading the processor would be a better idea over upgrading the gpu, but I'm not too sure. I could either give him a FX-6300 or a AMD 7850 from my current system.
 
Solution
The 7850 will probably be best, but that socket is pretty dated, and should have a complete overhaul. I wouldn't recommend the 6300 because it probably will not be much improvement. I'd be surprised if there is ANY improvement.

Again, a completely overhaul is probably best, but if it's not possible go with the 7850.
The 7850 will probably be best, but that socket is pretty dated, and should have a complete overhaul. I wouldn't recommend the 6300 because it probably will not be much improvement. I'd be surprised if there is ANY improvement.

Again, a completely overhaul is probably best, but if it's not possible go with the 7850.
 
Solution