The A6-3650 is basically a AthlonII x4 with more cache and made at 32nm instead of 45nm.
While the G4560 is a great budget cpu, it's not a real quad core.
http://www.3dmark.com/3dm/18577975
http://www.userbenchmark.com/UserRun/3364083
At stock the A6-3650 sorta sux, overclocked it catches up with the G4560 in mulitcore and quad core speed. Intel's kabylake single core speed is higher.
http://cpu.userbenchmark.com/Compare/AMD-A6-3650-APU-vs-Intel-Pentium-G4560/m1954vs3892
METRO REDUX BENCHMARK RESULTS
Options: Resolution: 1920 x 1080; Quality: Very High; SSAA: Off; Texture filtering: AF 16X; Motion Blur: Normal; Tesselation: Normal; VSync: Off; Advanced PhysX: Off;
Average Framerate: 69.37
Max. Framerate: 134.34 (Frame: 9392)
Min. Framerate: 22.22 (Frame: 8)
Some fsb overclocking with a better cpu cooler should get the cpu speed up. Drop the memory down to the next lower one but keep the timings and voltage for the faster speed. Mine is running at 1.475 volts with a CM212+ evo with a mod so it has 2 fans. 3.56ghz with the stock single fan and 3.61ghz with the extra fan.
The asus boards didn't go as high as gigabyte ones but you can still do some overclocking.
-YOU MUST RUN IDE COMPATIBILITY MODE IN THE BIOS FOR THE HDD BECAUSE THE SATA CONTROLLER WILL CRASH.
The HD-6870 is by far the slowest part of the system. A new cpu cooler, some overclocking, and a new much faster video card will help the most.
A card like the RX470,570, 480, 580 would be a huge upgrade and is as fast or faster than HD-6870 Tri-Fire.
A used GTX970 would be ok too.
-If you want to reuse your DDR3 memory a Skylake locked i5-6500 with a ddr3 board. Your better off putting the savings on not buying ddr4 memory into getting a i5 instead.
You will want to check this out too.
http://www.tomshardware.com/reviews/battlefield-1-directx-12-benchmark,5017.html
and
http://www.tomshardware.com/reviews/amd-radeon-rx-580-review,5020.html