yeah, the haswell is much stronger per core. It would also consume less power than an overclocked fx if that matters to you.
for the price of an i5, you can often find a xeon 1230v3 which is an i7 4770 with no iGPU, or you could get a used i7 2600k and z68 mobos are cheap now, and overclock that or even at stock the 2600k would be strong. You could even go with the ivy bridge xeon 1230v2 and an h61 mobo and be good or b75 mobo. There really hasn't been a huge improvement in CPUs since sandy bridge despite what the marketing says or upgrade happy enthusiasts like to spout >_>
for what it's worth, on 1080p ultra w/no msaa or at the very worst, 1080p high settings, since 2012, I've been able to play any game I wanted with my stock 3.4ghz i5 3570k and an hd7950 with 8gb ram, it doesn't take that much to play stuff on 1080p. I even tried an hd 7870ghz and it played bf4 64player multiplayer on 1080p ultra with no msaa at 60fps with my stock i5 3570k, and hd 7870/r9 270s are really cheap on ebay.
I think you'll be happy with the switch to an i5 or xeon (or 2600k and z68). I know personally I don't see myself even upgrading for many years, my current pc is still way stronger than the next gen consoles, and no matter if we like it or not, let's be real, most games are just console ports.