Written communication increases the possibility of communicating the same meaning to a large and scattered audience. If the written message is well written, so as to not be easily misunderstood or misinterpreted, readers will derive the same content from reading it regardless of their individual locations or situations. The key, of course, is that the message is written clearly.

Written communication demands thought and planning before it is commited to paper, computer, or whatever means of recording is used. That process allows for the crafting of the language, the development of expression or precision of wording that seldom occurs in verbal communication. The Declaration of Independence would not have had the magnificent language it contains if it had been delivered as a speech via Skype or other vocal means. Shakespeare's characters would not have presented the depth of emotion or the creativity of expression if the plays had been delivered without the benefit of a written script.

Written communication is clear, virtually permanent, and can be constructed with great care and attention to detail. It can be drafted up several times, proofread, and then sent off. However, it's fairly one dimensional. Written communication can't directly communicate tone. Voice and tactile sensation do a better job of getting across nuanced emotions. 

A disadvantage of written communication is that it is more time consuming and feedback is not necessarily immediate. Certainly, technology has helped this some, but in many ways, technology has also further hindered written communication. People are not as careful about what they write as they perhaps once were (for example, email is so much more informal than a handwritten letter).

Another disadvantage of written communication todayis a gross lack in writing skills. Many people who come across as perfectly intelligent in person reveal incompetency in written skill and are not taken as seriously. This problem also goes the other way around, however, and could also be considered an advantage of written communication.

Written communication is permanent. This can be both an advantage and a disadvantage. Sometimes you want or need to remember something. Sometimes you want to communicate to someone. In either case there is a huge advantage to writing something down.

Ironically, the importance of good writing skills in the business world has become more evident even as companies rely increasingly on computers and other new technologies to meet their obligations. (referenceforbusiness)

The use of computers to communicate has actually made the written word more common. Almost everyone now has to send e-mail at work, and the grammar is up for scrutiny.

We write more often, and more quickly. We can communicate more easily through the written word.  We can also pass on writing more easily and more efficiently.

I would say that the major advantage of written communication is that the person who is writing has the time to think carefully about what they will write.  They will not have any trouble with getting their ideas garbled as they try to talk in real time.  This can make the communication more precise and informative.

However, the problem is that the communication is not real time.  The reader does not have the ability to ask questions.  They do not have the ability to read the writer’s body language to help understand what the writer is really trying to say.

Thus, writing is more precise, but can cause difficulties because it is not face to face and real time.