Come on, not all intel cpus are that expensive. An i3 would be ideal for this, since emulators like fast single core performance, and that is the strong suit of an i3. An i3 haswell is very close to the higher end AMD APUs in price. The problem with intel is that he would need another motherboard as well. You would also need a discrete gpu with the i3, but you probably do as well with the APU.
Adding a discrete GPU would be the logical first step. We are still not getting a very good description of the full system specs. OP, can you download GPU-Z and find out what the graphics is, or do you know if a discrete card has been added? We also need to know the wattage of the power supply. It should be posted on the side of the unit. Look for the numbers listed under the +12V category. Is this an OEM box or did you or someone else build it? If it is an OEM box with a weak power supply, something like a GTX 750 or 750Ti or HD7750 would be the only cards that could run on an OEM PSu. If the power supply is a good quality one of 400 amps or so, you could go higher like an R7 260.
I definitely would not upgrade to another AMD APU from an A10-6800k. The improvement will be minimal in cpu performance, maybe 10 or 20 percent, and maybe something more in graphics, but not a huge amount. You could try overclocking, but you would need a better heat sink, and have to make sure the power supply is sufficient. Even then, you will only get 10 to 20 percent performance from this, so I dont think it is going to be a huge difference. Ram speed and whether it is dual channel or not can also affect the performance of an APU quite a bit. OP, is there any way you can find out this information?
Edit: Sorry, you did give the memory specs. I did not see that. That is pretty fast and I would assume dual channel, so you should be good there.