So the i3 has faster clock speed and better integrated graphics chip, it also has a few more instruction sets.
The only thing the g4560 has going for it is that it is cheaper and supports higher frequency (2400mhz vs 2133mhz) memory natively.
The g4560 will require a 2xx serries board (so h270, z270,b250). While the 1xx serries will support it, the will require a bios update which you cant do without a skylake CPU.
If you want to get a 1xx serries board then go with 6100.
If you can get a 2xx serries board I would look at the g4620 which has same clock and igpu as i3-6100 but support for faster ram.