The stabilization of asphaltenes by chemical additives, resulting mainly from the action of amphiphilic molecules with low molar mass, has been widely used in the petroleum industry. Polymer materials can also be used as asphaltene stabilizers, although they can act as stabilizers or flocculants in function of their molar mass and/or composition. Asphaltene flocculation is also important in deasphalting crude oil or recovering polyaromatic molecules to be used as filler in polymer composites. In order to better understand the factors that affect the action of polymers on asphaltene phase behavior, we investigated a new family of compounds based on styrene-octadecyl methacrylate and styrene-octadecyl cinnamate, with varied sulfonation degrees. The results show that besides molar mass, the content of long pendant hydrocarbon chains (C18), the sulfonic groups content in the molecule and the polymer concentration directly influence the type of effect (stabilization or flocculation) on asphaltenes. The sulfonation of copolymers increases their stabilizing action by promoting stronger interaction of the additive with the asphaltene molecules by sulfonic groups. However, an excess of sulfonic groups promotes a reversal of this behavior, from stabilizing to flocculating, because a large amount of sulfonic groups in the same molecule brings the asphaltene molecules together and induces their aggregation.