The Warriors did a good job of bringing the brawler into last generation, after a long absence. (Urban Reign is a better brawler but with less "meat" despite its superior depth.) Red Dead Revolver was not bad for an atmospheric western shooter, but shallow and largely based in repeating a mission until the spawnpoints are recognizable; never a formula which engenders affection from me. San Andreas is a good game, but instead of bringing any new or varied gameplay, it falls victim to the trend established with Vice City: thinking bigger is better, and adding a needlessly filigreed rococo level of detail to gameplay established in the predecessor.
What Bully did is to take the GTA formula, comprehend the basic model of what makes it attractive, then successfully adapt it for a younger audience WHILE varying the gameplay and telling a more coherent story than San Andreas or any other GTA (VCS, LCS) until GTA IV, which itself eschews most of the side missions solely to focus on the story.
In short, Bully evolves the formula and proves that it's not based on hiring hookers, killing them for the cash you just gave them, and running drugs and killing Cubans. Bully proves that the sandbox formula can be compelling for both story and side missions, all of which are offered in an internally-consistent format to the game world's logic and presentation.