That's an interesting question. We happen to be working on this in class at the moment as the students are writing narrative paragraphs, so I had some of the students do some storytelling and then we discussed the differences between ASL and academic English narratives.
I think there are some qualities of hearing storytelling that transfer to ASL storytelling. Poise, communication with the audience, enthusiasm, ability to set a scene, a feeling for the action of the story (rising, climactic, falling, etc.), energy, enthusiasm, and acting skills are all things that make a good storyteller in either language.
However, spoken English storytelling tends to rely on the play of words to create the mood. A large vocabulary helps so that the exact right adjective, for example, can be chosen to get your point across most effectively. By comparison, ASL storytelling is of course visual. The best ASL storytellers have mastered the use of space, and that is the medium used to get the point across most effectively.
I think if you're a bad storyteller in English you might not be a good one in ASL. However, if you're a good storyteller in English, you still won't necessarily be a good one in ASL!