Our feel from the beginning was that the Athlon X4 880K was actually an A10-7870K with the integrated video disabled and 100 MHz more clock. Our tests were consistent with that: the Athlon X4 880K performed barely better than the A10-7870K, but the difference was so small that we can consider both the CPUs were similar in performance.
Comparing it to the competitor Pentium G4400 (remember that the direct competitor of the Athlon X4 880K is the Pentium G4500, which has 200 MHz more clock than the Pentium G4400), we concluded that, while each core of the Pentium has a higher performance of an Athlon core, the fact the Athlon X4 880K has four cores made a difference on some applications. So, in programs that use one or two processing cores, the Pentium G4400 (and, consequently, the Pentium G4500) is a little faster, but in programs that uses the four cores, the Athlon X4 880K has a higher performance.
On the games we tested, it was also clear: on one game the CPUs were on a tie, on two titles the Pentium G4400 was a little faster, but on three games the Athlon X4 880K performed better. Keep in mind that, in our tests, the integrated video was disabled and a mainstream video card (GeForce GTX 950) was used.
After all, the Athlon X4 880K is a good buy? Yes, if you are building a computer for gaming or working, with a dedicated video card, and need to focus on cost/benefit ratio, it is a good processor.
Particularly, if you are thinking about building a computer based on an AMD A8 or A10 CPU, but want to disable the integrated video and use a mainstream video card, the Athlon X4 880K is a better option.