Never had the opportunity myself, however, I agree with nweismuller.
The Rich tag should basically mean, these guys have something to lose. That something has value, to them and to other people. It means they're not so desperate on the edge of life and death, but it also means they keep circling what's important to them. It changes the focus what can find on the road today, will it be enough. to: Did we find what we were looking for? Did we keep everything safe?
For me richness tends to mean they become localized a bit more. They have a place, and that place has stuff. It's not the Choppers stuff, its the gangs stuff. Thus its not like a hardhold. In this case, maybe its just families, crops, land, whatever. But while rich chopper gangs might not be as desperately aggressive, they're still very much protectively aggressive. It becomes a lot more about what keeps them rich then how to get rich in the first place. Anyway, this will have very real effects when it comes to what orders the gang might resist, and for what reasons they might resist them.
In short, a Rich gang does not mean the Chopper doesn't pay his share. His gang doesn't support him. They each support themselves together.