I had the G551JM (pretty much same, with slightly older gtx860m and 4710hq cpu) for 2 weeks and eventually returned it. It was quite well made piece but after using it I realised it cant deal with the heat at all. I occasionally played GTA 5 on it and its components managed to get very hot rather quickly, about 15 minutes playing the CPU reached 97-98 degrees celcius, GPU reached to 86 degrees. CPU started to thermal throttle and eventually gaming experience was not so great anymore. Since I was hoping to use this PC more than 2 years, I was not believing it could even last that long with those temperatures. I contacted the reseller about the problem and they agreed with me and I was able to return it. Then I realised that this 15 inch laptop with single fan is no way capable of handling such loads for Asus´s advertised "gaming marathons". I then got the G750 which coped with the temperatures very well, unfortunatly that piece had motherboard fault and I had to return that also, but thats different story.

My point is that if you want to give this G551 some heavier loads constantly for many hours, it very likely gets unstable and I bet you would not be satisfied with it at all. I havent owned that G501 but according to Asus´s website it has dual fans with proper heatsink so I think it might cope with the heat problem better than the G551.

My realization is that there is only one true Asus gaming laptop that can withstand the challenges - its the G751 with very good cooling system.
But If you really want thinner and 15 inch laptop then I would go for the G501 because it seems to have better cooling system. Although the price difference is too big in my mind.