I would go with the second option. Newer graphics and processor, which if not a little faster, may contain some power savings over the predecessor. I think the 8GB upgrade option (or higher) is there for the G4-2012 model. HP is making it difficult to tell, but it seems backwards to not include this option.
Big B is right, The second one is Upgradable to 8 gigs of ram.. BUT if you want a Gaming Computer you don't want a Brand Name computer, You want to Build One yourself with High end parts..
Agreed with B. Second option is slightly better. Newer gear even by a little bit might solve some poor compatibility issues that some games or software have. The newer the game, the worse the compatibility it seems.