What is my bottleneck?

Solution
Those are two of the most demanding games, so you'd have to turn down the quality settings to roughly MEDIUM though I can't give an exact answer.

As for the bottleneck, that's a slightly tougher question because:
1) The CPU would be a definite bottleneck with a better graphics card, but
2) The graphics card would be a definite bottleneck with a better CPU.

It's very possible that for both games the CPU would be a bottleneck at times (i.e. in Multiplayer BF4 especially) but that the graphics card would be a bottleneck at other times.

That's a very confusing way of saying they are arguably BALANCED and likely a good match at this budget.

*I'll see what I can put together on pcpartpicker for roughly the same price.
Those are two of the most demanding games, so you'd have to turn down the quality settings to roughly MEDIUM though I can't give an exact answer.

As for the bottleneck, that's a slightly tougher question because:
1) The CPU would be a definite bottleneck with a better graphics card, but
2) The graphics card would be a definite bottleneck with a better CPU.

It's very possible that for both games the CPU would be a bottleneck at times (i.e. in Multiplayer BF4 especially) but that the graphics card would be a bottleneck at other times.

That's a very confusing way of saying they are arguably BALANCED and likely a good match at this budget.

*I'll see what I can put together on pcpartpicker for roughly the same price.
 
Solution
Hi,
I had a more expensive build done for someone else, but I'll just link it here as I have to destroy it to create another one.

This one has a similar graphics card (GTX750Ti roughly equals HD7850) but a much better CPU. It's the CPU that really raises the price, but it will make a big difference in some games, especially in the future if you drop in a better graphics card.

I'll post another build after this one:

http://pcpartpicker.com/p/3tf5H
 
Update:
I can't beat the price of that Combo when you factor in BF4 so if that's your budget I don't think you can beat the price.

You'll still need:
a) DVD burner, and
b) Windows (Recommend Windows 8.1 64-bit)

You may wish:
c) better CPU cooler: Cooler Master Hyper 212 EVO

*BF4 has code added to work better in Windows 8. I recommend getting Start8 to bypass the new interface if you wish (I do).