Well, if you can afford it and want to...sure!
If you scrap it, I would go for Intel though, offers more atm and you are guaranteed to get an upgrade for the next gen CPUs (Broadwell).
Although, keeping your PC and just upgrading the CPU has one advantage too...you can dual-gpu (hybrid crossfire) with your existing 7750 for the Kaveri/Richland APUs, although not all games benefit, some result in even lower fps. The scaling is not that great but boosts your performance quite a bit in any case. But dual GPU solutions always have their own sort of issues too.
You can also get the Athlon X4 i mentioned. It should be the same CPU that a10- 7850k has but without GPU part, so you can buy yourself a nice dedicated GPU.
1. New PC. = Most performance, costly
2. Athlon X4 = easily more performance than APU upgrade, you need this CPU + dedicated GPU (you might try the current one and see if you are happy about it or not, and then upgrade if you wish)
3. Get A10-7850K. Probably the cheapest one but also the least powerful option, and there is essentially nothing more powerful for that socket atm. To get most of it you need a 2400+ MHz RAM though.