General

Personally I would not take this because of a lot of outdated things. You can very easily find another Asus laptop for the same price but better specs. I see somewhat outdated things such as the 1366x768 monitor and the graphics card. The laptop itself is a perfectly fine machine but I feel there are better competitors out there for the same price range.
I found this one for less which is a pretty beefed up version of the one you found
https://www.amazon.com/K501UW-AB78-15-6-inch-Full-HD-Gaming-Glacier/dp/B01DT49XN8?tag=slickdeals&ascsubtag=8242439245b011e6b7294627076903cf0INT
This one has a better processor, graphics card, and screen. The storage may be a topic worth debating because SSD is much better in terms of speed like startup and stuff like that but will gradually fill up. I would say to keep looking for what tends to your needs

Depends on what you plan to run on said laptops. The 920M runs some games better than the 820m (Over 60% faster according to http://www.game-debate.com/gpu/index.php?gid=2895&gid2=2758&compare=geforce-920m-2gb-vs-geforce-820m-2gb)

I'm no computer expert, but both of these laptops are actually very similar they have the same RAM space of 8GB, resolution, similar but a bit different USB ports, Hard Drive Capacity/Storage of 1TB and they both look like they are suitable for gaming. They do have a different operating system though (if that matters to you) The Assus F555LD 15.6" Intel Core has Windows 8 and the other one is Windows 10. They both use NVIDA as a graphics processor NVIDIA® GeForce® 820M with 2GB DDR3 VRAM (Assus F55LD) and NVIDIA® GeForce® 920M(Assus F556UJ). They also both use Intel Core i7 which is ideal for gaming. I think go for the cheaper one of the two in that they are both similar in almost every component. I'm actually thinking of buying a laptop soon but I'm still debating on whether to get a Dell laptop or Asus