Which processor is better for gamin pc and also durable

For gaming, the I3 has shown to beat the FX because of its single-core performance. 6300 is better for multithreaded tasks. Durability? Well, the I3 has a lower TDP, so if it's cooler I guess one could say theoretically it's more durable and will last longer, but any CPU should last 10+ years.
 
I would choose the 6300 as it is not limited by core amounts for games that need 4 cores, and has the over clocking benefit- you can get some serious gains in performance that way, however the 4130 has the advantage of faster cores, but less of them, so if you are only playing games like counter strike, you will be much better off with that cpu. Neither of them are any more durable, it all depends on the voltage they run at, and cpus rarely "die" in their lifespan- they can live for 2-5 years depending on the voltage you put through them- the more voltage the shorter the lifespan, but the better overclocks and speed you can get. The 4130 is not overclockable
 
A good integrated circuit should have a near 25+ year lifespan. I have at least one computer from 1984 that is still working. Meaning every single IC and memory chip has survived the test of time. More common for things like capacitors and power supplies on board PCBs like motherboards to fail before the IC.

These smaller lithographies haven't been around that long, so there isn't much data on how quickly they will break down from voltage wear and tear, but they operate at a much lower voltage than previous generations.
 
As for the AMD vs Intel. The AM3+ socket is end of life. If I had to buy it now, I would go straight for the FX-8320 or FX8350.

LGA1150 socket is also end of life, but there are processors available beyond the i3, so you have some future upgrade options.

Ideally if you were to go the i3 route, you should pick up an LGA1151 board and 6th gen processor. That will keep your upgrade path open for that much longer.