Your pc initially had a 300w psu.
Tp run a R9-380, you probably also replaced the psu with one in the 500w or higher range.
For a significant graphics boost, you are looking at a GTX1070 class card which is some three tiers higher on tom's gpu hierarchy chart.
https://www.tomshardware.com/reviews/gpu-hierarchy,4388.html
Your $500 budget should handle that.
As a test,
Run HIS games, but lower the resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely more cpu limited.
If you are cpu limited, The best you could do would be to replace the cpu with a I7-3770K.
I would not do that, the new 8th gen processors are so much better