This was a question a participant in a storytelling workshop asked the other night. My answer then was nowhere near complete, just as what I write here also will miss some salient points. Here's what occurs to me now:

Oral storytelling 

• Is an older artform than written.
• Does not require that the listener be literate.
• Requires teller and listener to be in the same place (hmm, unless it's on a recording, which places it closer to written).
• Is not in set form. The storyteller may change the story depending on the audience, circumstances, time allotted, mood of the audience, mood of the storyteller, venue. 
• May be more concise--too much detail can bog the experience down.
• The storytelling/story listening experience is usually shorter. Of course there are exceptions for cultures in which epics may last over days, or with serial stories.
• Depends on nonverbal as well as verbal communication--facial expression and body language, volume, pacing, attitude, etc.
• May use repetition and mnemonics to help the audience remember people, places and action.

Written storytelling

• Requires literacy. Even with a read-aloud, somebody is reading it. 
• Is usually experienced by the reader without the writer being present. The writer is unaware of the reaction of the reader.
• Is in set form in each edition (with some exceptions for online experiences).
• Requires the writer to show attitude, emotion, etc. using words.
• Have a wider range of length, from flash fiction to multivolume sagas. 
• The reader may flip the pages back to remind herself of something that happened earlier. 

Of course, a good story is a good story. One artform is not better than the other. Oral storytelling can enhance writing and writing can enhance oral storytelling--I often write about the stories I tell, in order to understand them.

What did I miss?