The processor is the biggest difference. Though it says both are an i7 Processor, the difference is in the performance. The Acer has an Intel Core i7-4510U. The "U" indicates ultra-low voltage meaning it'll use less power (longer battery life) and it'll produce less heat, but this hinders performance.
The ASUS has an Intel Core i7-4700HQ, which means high performance ("HQ" designation). This type of mobile processor is made for the best possible performance versus the "U" and it's focus on battery and heat efficiency.
The battery life advertised for the Acer is 6.5 hours, which is 1.5 hours more than the ASUS (5 hours advertised). This is due to the Acer's energy efficient mobile processor.
For LoL, the Acer should run great, without any hiccup, but for the best performance the ASUS is a clear winner.