This is such an interesting question! Let's see if we can think through five advantages and five disadvantages for these two vital forms of storytelling.
First, when we tell a story, as opposed to offering it in writing, we are able to adjust to our audience in our style, a disadvantage for the written story. We will tell a story to a young child in a very different manner than we would to an adult. We might make the story shorter, eliminate some racy aspect of it, and choose simpler vocabulary. This is a distinct advantage over words that are "frozen" on the page, thus conferring a disadvantage upon the written word, since the written word cannot be changed on the spot.
Second, when we tell a story, this allows us a physical intimacy and immediacy that are not gained with a written story. The act of reading is by its nature a solitary act, while storytelling is a social act. Even for reading aloud, the reader's eyes must drop down to do the reading, a barrier between the reader and the audience. Oral storytelling, even if the audience does not speak, creates a kind of dialogue between audience and reader that is personal and here and now.
Third, oral storytelling is evanescent, while the written story persists in a form that can last for thousands of years and can travel around the world. We are still reading stories from the ancient Romans and Greeks, for example, and routinely read stories from all over the world. In fact, if we ever get to Mars, we can take our written stories with us! The written word has a powerful advantage this way, while the story told disappears.
Fourth, because of the fleeting nature of the spoken word and the enduring nature of the written one, people can make meaning more easily of the written word than the spoken one. Listening to a story is a very different kind of act from reading a story. I hear a sentence and the words are gone. Someone next to me laughs, and I miss the words. I hear something I like, but I cannot focus on it for an extra second because more words are coming. But I can read at my own pace, slowly or quickly or somewhere in between. I can read a passage more than once. I can go back and check on the name of a character. I can even cheat and see what the ending of the story is. As I have these freedoms, the story can be far more meaningful to me than a story I have heard. I am able to take the time to make connections with other stories I have read or with events in my own life. The written story is able to resonate in a way that the story told aloud simply cannot.
Fifth, a disadvantage to oral storytelling and an advantage to the story told in writing is that the latter has far more utility for someone who seeks to polish writing and reading skills, which everyone should want to do. When we read, we can come to understand far more easily how a story is constructed. When we read, we can learn new words that we can use ourselves. When we read, we expose ourselves to different styles of writing. All of these are helpful as we read more to become better readers and we practice writing. We can emulate a style. We can create a plot line more easily. We come to understand how to show a reader a character or an idea. Some of this might be glimpsed in passing with a story told orally, but it is far less likely.
For thousands of years, we could only tell stories orally. However, once we began to write, oral storytelling was by no means abandoned because, as you can see, it continues to have some powerful advantages. Reading a story has other advantages, which we would never want to give up.