The way I see it, Franklin is more like Luis Lopez from TBoGT, but at the same time, very different. Luis wanted to move out of the criminal world and into high-society business side of Liberty City. Franklin, in contrast, wants to be a motherf*cking boss. Instead of out, he wants to move up. And their supporting friends are counterparts to each other; Lamar and Armando. Lamar sees gangbanging as his heritage and doesn't think Franklin should betray his background. Armando said the same thing to Luis, stating that he shouldn't pretend to be a "big-shot" and should stay true to himself.
Franklin has merely upgraded. He's leaving the bullsh*t behind him and is striving heading for more, which is why Rockstar describes him as ambitious. Franklin wants more. And he isn't being greedy about it, as you can see that he wants Lamar to move up with him as well. But we know how that is.