Ooh that tough, the 6100 has much stronger cores but on 2 with hyperthreading. I'd actually expect the 6100 to be better in most games. IPC counts for games.
The i5-2400 will not have any advantage over the i3-6100 in gaming. Much slower cores make it the same or less than the i3-6100. So I would go with the newer tech.
As there is no unlocked 2400 you are limited to blck overclocking. 3.8 is unlikely. Even if you managed it the IPC of the 6100 is about 30-40% higher so the 2400 single core performance would still be 30-40% behind.
How about i3 and upgrade cpu down the line?
At least it puts you on the more modern platform.
The IPC difference between skylake and sandy bridge is about 20%, but i would like to see you upgrade to a better processor if you have the GPU to match it.
I wish we have improved that much, but from the tests i have seen, pure ipc at clock for clock was 20% give or take depending on the application.
30-40% would include clock speed on top of it, perhaps that is what you are thinking?
Pentium G4560 w/ B250 motherboard would be cheaper than an i3-6100 while being very close to the same performance. The thing is we don't know if the OP is building his own or buying pre-built. From what he's said, I assumed he was buying pre-built.