Compairing Apples & Eggs.
I didn't realize that Haswell had so many extra instruction pipes, so I went looking for details to make a clearer picture of the landscape.
Phenom II : max 3 ALU instruction per clock per core, max 4 instructions per clock per core, [ 3x ALU 3x AGU (3 max per clock), 1x 128 bit FPU per core ]
Piledriver :max 4 ALU instruction per clock per module, max 5 instructions per clock per module, [ 4x ALU 4x AGU (4 max per clock), 1x 128 bit FPU per module ]
Haswell : max 4 ALU instruction per clock per core, max 8 instructions per clock per core, [4x ALU, FPU(2x 256-bit FMAs or FMULs, 1x 256-bit FADD per clock]
Multi threaded:
Example Phenom II 980 @ 3.7 Ghz:
max ALU rate: 4 cores x 3 ALU x 3,700,000,000 Hertz = Theoretical max, 44,400,000,000 ALU instructions per second.
Example AMD FX 6350 @ 3.9 Ghz:
max ALU rate: 3 modules x 4 ALU x 3,900,000,000 Hertz = Theoretical max, 46,800,000,000 ALU instructions per second.
Example Intel Core i3-4160 @ 3.6 Ghz:
max ALU rate: 2 cores x 4 ALU x 3,600,000,000 Hertz = Theoretical max, 28,800,000,000 ALU instructions per second.
Single Treaded:
Example Phenom II 980 @ 3.7 Ghz:
max ALU rate: 1 cores x 3 ALU x 3,700,000,000 Hertz = Theoretical max, 11,100,000,000 ALU instructions per second.
Example AMD FX 6350 @ 3.9 Ghz:
max ALU rate: 1/2 modules (1 core) x 4 ALU (2 ALU) x 3,900,000,000 Hertz = Theoretical max, 7,800,000,000 ALU instructions per second.
Example Intel Core i3-4160 @ 3.6 Ghz:
max ALU rate: 1 cores x 4 ALU x 3,600,000,000 Hertz = Theoretical max, 14,400,000,000 ALU instructions per second.
(Ignoring the fact that the Haswell core can not always utilize all the ALU pipes due to some instructions needing to wait for each other)
So the very important for games ALU throughput of these CPU's is quit different, theoreticly the Core i3-4160 can muster 2x the ALU performance over the FX in single treaded situations clock for clock, in multi treaded scenarios the tables get turned how ever.
The gaming future is multi treaded though, most new and exciting game titles will be optimized for 4 cores, with game engines on the horizon being optimized for 8 cores.
So the question becomes then do I need a CPU that is fast with old games that are single treaded, or will the CPU be of more use in newer more highly treaded scenarios, I personaly would still go for the FX as I can forsee it will be more usefull in newer titles, and that single treaded games mostly will not need a beefy CPU in the first place.
The Core i3 is how ever build on a smaller proces making it more power efficient, so if power efficency is your thing go for the Core i3, allthough you might not be able to play certain titles and more new multitreaded games it will suffer, if you do not mind the small extra power overhead of the FX and want to be a bit more future proof go for the AMD FX.