Why choose Intel Pentium G4560 over your older i3 and i5 model? The answer here is "Value". This is the very first time you hear in 2017 that Pentium undergoes Hyper Threading technology and with that 2 Core 4 Thread norm in this spectacular budget CPU, you are actually comparable to those with i3 7th gen users in mind.
It also uses Kaby Lake as it's name for the processor and it's widely new. Here's a quote from several online articles that has proven that G4560 is worth your 2017 budget and the slow economy across the globe.
Quote from Eurogamer.net:
"To test the Pentium G4560, we put together a budget-orientated PC gaming set-up. The Z270 boards we've previously used for reviewing the unlocked Core 'K' chips are replaced with a more modest MSI B250 Mortar board. The B250 chipset has no CPU overclocking facilities whatsoever, making motherboards based on this set-up better suited for a budget build. However, the B250 chipset has a secret weapon - support for 2400MHz DDR4 memory, compared to the 2133MHz limit on RAM imposed on all Skylake processors. We've yet to confirm it, but even cheaper H110 boards may support 2400MHz RAM too - but it will require an updated BIOS.
But the point is that this support for additional memory bandwidth is significant. Prior Digital Foundry processor reviews have found a distinct relationship between CPU performance in gaming and faster memory. This is especially significant for lower-end chips like the Core i3 line and the Pentium G4560 - because you are far more likely to be CPU-bound using one of these chips, so anything that can push up lowest recorded frame-rates is obviously a good thing. And this is borne out in the benchmarks where the move from 2133MHz DDR4 to the new 2400MHz standard effectively allows the Pentium to overcome its clock-speed disadvantage against the Core i3 6100. In six out of the seven games we tested, the G4560 with 2400MHz DDR4 matches the performance of an i3 6100 paired with slower memory."