DrLexus :
i3-4160 pairs better with an r9-280 and modern gaming.
I find it ironic how everyone says overclocking can save you money. Almost everyone that overclocks ends up spending so much extra money on extremely high end motherboards and coolers that any money saved on the processor is moot. Don't get me wrong, overclocking is fun and interesting, but don't go into it for the idea of saving money.
The i3-4160 is a solid processor that will hold up just fine with an r9-280 in most any modern game, and you can pair it just fine with a reasonably priced H97 board--no need for Z97. Also, while the G3258 is a great processor, there are some games out there that will not run well with just 2 threads, no matter how fast your single thread performance is.
So if you want a gaming machine, go with the i3-4160. You can build a separate G3258 PC later on to mess around with clock speeds if that's something that interests you. BTW, I own both of these processors as well as an r9-280, so I'm not just spitting untested theory at you.
You seriously think that a dual core with hyperthreading will give that much increase over a dual core w/no hyper threading? Because it won't, maybe if you're comparing a four core four thread I5 to a six core 12 thread I7 or something, or even a quad core I5 vs quad core 8 thread I7 would give decent improvement. But when you still only have two physical cores, all the threads in the world won't make "too" much difference.
You would honestly be far better off getting a used/open box sandy bridge I5 or something on the cheap. A decent I3 hyperthreaded cpu will put you back ~$120-150ish, at that point you might as well save up and get an I5 4690K or something for ~$200, or just go with an 8 core amd for the same cost as the I3 which would help you in rendering applications etc.. over the I3 for a minimal to no loss in gaming performance as a good I3 (~$150) is roughly equal gaming wise to an FX-8320 or something (~$120) but you'd get better rendering and editing performance.
The whole point of OP's question is whether the I3 gives enough performance increase over the Pentium anniversary to be worth the nearly double the cost that the I3 has. And quite honestly....NO, it doesn't. Would i still go with an I3 for my rig? Yeah, definitely, but i have the money to do so, while OP might not. And if you're limited on cash you'd be much better off saving that ~$50-70 extra you'd spend on the I3 and getting an R9 280X instead of a 270X or getting a GTX970 instead of a GTX960 etc.. since an overclocked Pentium will still not bottleneck a single 280X/290/970 in over 90% of cases.
And as far as motherboards, you can get decently good Z87/Z97 boards for under $100, so that's not really a valid point tbh.