Biggest bottleneck in my system?

Okay so I've recently upgraded my GPU to Radeon HD 7870 but naturally the rest of my system doesn't seem to be able to keep up with it, hence Battlefield 4 not running too great on any of the good settings.
My system is:
i3 550 @3.2GHz
Sapphire Radeon HD 7870 GHz edition
12Gb 666MHz Kingston RAM
500W coolermaster PSU
7200RPM Samsung hard drive
Standard Dell Inspiron 580 Motherboard

I'm thinking about upgrading my motherboard to Gigabyte GA-970A-UD3P with an AMD FX 8320. Would this be the best way to solve the problem of low FPS in my games?

I peeked into your other thread that ended up discussing this issue already and agree it is the CPU (I would have kept on in that thread, now you have two going in the same direction). I would also upgrade the RAM as well to 1600/1866 sticks, nothing faster.

The 7870 is a solid mid-range card, but may struggle a bit in modern titles itself, for example, BF4. What FPS are you looking for 60+ all the time or anything over 30? What resolution do you game at?

EarthDog said:

I peeked into your other thread that ended up discussing this issue already and agree it is the CPU (I would have kept on in that thread, now you have two going in the same direction). I would also upgrade the RAM as well to 1600/1866 sticks, nothing faster.

The 7870 is a solid mid-range card, but may struggle a bit in modern titles itself, for example, BF4. What FPS are you looking for 60+ all the time or anything over 30? What resolution do you game at?

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I thought a clearer title might get some more attention!
Would faster RAM really be worth it? Because we can be looking at around £70 for a couple of sticks! Would it improve fps? I'd like 60 and above really, that's where it's going to be nice and smooth, although I'm not fussed about running BF4 on ultra, just maybe high at 60fps.
I game at 1080p because I really don't like anything less on my full hd screen

Anything over 1866 will really not improve FPS. The jump from 1600 to 1866 is negligible as well but the price difference is too. But running 1333 will leave some performance on the table for sure.

EarthDog said:

Anything over 1866 will really not improve FPS. The jump from 1600 to 1866 is negligible as well but the price difference is too. But running 1333 will leave some performance on the table for sure.

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That's worth considering then. As for the processor and mobo, do you reckon that'll make a decent difference for now?