The i3s would be better in most games than the i7. There wouldn't be a noticeable difference between the two i3s.
If you want an i3, look at the i3 6100.
I'm in same position here. Old generation i7 or a newer i3. They are in the same price range, and Skylake exceeds my budget. Looking to play mostly singleplayer games like GTA V, Dragon Age, Need for Speed paired with GTX 750 Ti probably. So would you recommend Haswell i3 over Nehalem i7?
the i3s because they are based on a newer architecture
with hyperthreading, higher clock speeds and more instructions per clock, which means better gaming performance I wouldn't care about the fact that the i7 you mention has 4 cores