I also think "говорить по-русски" is preferable. The phrase "по-русски" means "the way Russians do it" and its primary usage should be in that meaning. For example, Ramil's signature says: "Стриптиз по-русски - я плавно снимаю с себя всякую ответственность". So, when you say you speak the way Russians do, that means you speak Russian the right way. However, when you say: "говорить на русском языке" that might also mean it's easy to understand you, even though you probably use the words not the most elegant way possible. Therefore, "я тебе русским языком говорю" is a synonym for clarity.