If APU stood for Advanced Processing Unit, you would have thought that APUs would have a performance edge over discrete processors & GPUs, but they don't.
Depending on the circumstances, the answer will vary. I believe a CPU and dedicated graphics card combo is preferable to an APU for the vast majority of users.
When it comes to gaming computers, APUs are a great way to bring two birds together with one stone if you don't want to spend a lot of money on a new one.
In the end, APUs will never be an ideal choice for gamers. The high-resolution gaming capabilities of dedicated GPUs enable higher resolution gaming while eliminating the burden on the CPU.