Well, the 6500 will perform very well, and is more than enough for a GPU like the R9 380. In the short term, you probably won't really notice a difference in performance. In the future, if you upgrade your GPU and/or your CPU starts getting old, the 6600k might have a little more staying power. You're looking at $20-30 extra for the CPU, plus ~35$ for a decent cooler like a Cryorig H7. Up to you if that's worth it. You could justify it by saying you're looking to get the most life out of your current platform and view that cost as being spread over the the whole duration you'll be using the CPU (years).
Do you like the idea of OCing? If it's something that interests you in itself, that would would make the decision easier, haha.