Perfomance issues with MSI's Radeon RX 480 powered by AMD

So i recently got my RX 480 4gb gddr5 a few days ago and have been loving the perfomance out of it. I have been playing skyrim on high details no problems same with Diablo 3 and paragon. But for my favorite game Overwatch i'm having issues. I have to set everything too low to get a decent fps. In load screen i get like 150+fps but then in game im around 40-50 then in team fights i drop to arouns 20-30. It kinda sucks and i'd like it to be faster. Could it be my cpu isn't very good? It's an AMD A6-3650 2.6GHz. i also have 8GB RAM and running windows 7 64-bit. I don't have a ton of knowledge with this subject just basic stuff but i really don't understand why Overwatch is so slow when i can play these other games at high or ultra details with no problems. Maybe someone here could help me out. In my opinion i think it's my cpu but i have had friends say i need more RAM but i just don't know to be honest.

My guess is the CPU may be bottlenecking the system, and I think it is. Do you still have your previous card or can you borrow something stronger from a friend just to check? If you end up having similar fps in games and scores in benchmarks or at least the curve is significantly flattened, then it's likely the CPU bottlenecking you. Then there are also some games that depend on the system clock heavily, to the point that they favour Intel's cheap Pentium G processors just because their clocks are faster than on the i3s from the same generation. An otherwise high-performing but low-clocked CPU can be out of luck with those games. Also, large fights tend to decimate the framerate in what looks like a fluidly running RPG or shooter, alas.

Overwatch recommended ram requirements are 6GB.

GPU is a GTX 660 or AMD 7950.

https://us.battle.net/support/en/article/Overwatch-System-Requirements

It's the CPU no doubt, 2.6ghz is a low clock, and that CPU has terrible performance per core to begin with. ie even at 4ghz it will lose to a current intel cpu at 2ghz.

http://www.anandtech.com/bench/product/403?vs=1829

It's not good enough for gaming imo, I'm surprised it even plays Skyrim well.

AMD APU is the problem here. Overclock the snot out of it, or upgrade. I'd upgrade...

http://www.techspot.com/review/1180-overwatch-benchmarks/page5.html