After reading your post, I picked one of my favorite games, GTA 3, and looked up how well it runs on the Note. It turns out, it's not compatible with the Note

XDA has a thread describing in detail how to get GTA 3 on the phone (download it illegally), and another thread describing some bad stuttering problems people are experiencing after going through the trouble of getting it installed.
Based on my experience, from asking friends to show me games on their Android phones and researching online, this seems to be the norm for playing any advanced game on the platform.
Curious, I just looked up Real Racing 2, but it too is not compatible with the Note. There's an XDA thread full of people installing and uninstalling drivers, switching ROMS, downloading the game illegally with data sets from diffent phones, manually renaming and moving files...etc.
Most of the games I want to play, aren't available anywhere else but iOS. Of the games that are on Android, there's a good chance it won't run on my device. If I'm lucky and it does run on my device, there's a good chance it will have performance issues.
When people talk about fragmentation, this is it. Even if the game is Android supported, it's not supported on all devices. It doesn't sound like a good experience.