A quick and dirty way is to look at the passmark numbers.
For example, your A8-7650K has a passmark performance rating of 4931 and a single thread rating of 1423.
https://cpubenchmark.net/cpu.php?cpu=AMD+A8-7650K&id=2489
By comparison, a i3-6100 which is an excellent mid-range gamer has a passmark number of 5414 and a single thread rating of 2102.
https://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i3-6100+%40+3.70GHz
Most games can use only 2-3 threads and most are dependent on the performance of the single master thread.
You buy a APU for the excellent integrated graphics.
But, there are no real good upgrades, particularly for a gamer.
If you install a superior discrete graphics card, you will have thrown away the big advantage of the APU.
Then, you are left with a relatively weak cpu. Most games depend on only a few fast cores.
The possible upgrades are to more cores, but few games will use more than 2-3 cores so 6+ cores are not very helpful.
Bottom line.....
What you get with a APU is what you will live with forever.
Virtually any gaming pc will use discrete graphics.
Why the difference if clock rates are similar?
It is because the intel architecture does more work per clock cycle.
And.. to answer your implied question, $200 buys you something like a GTX1050ti which is decent for 1080P gaming.
To get an idea of what you might expect, look at this review of the i3-6100 which includes comparisons with your A8-7650K and a variety of graphics cards.
The GTX770 is probably the closest comparison set of tests.