I suspect the persuasiveness in oral communication is related to our susceptibility to favorable impressions of people who mimic our tone, posture, etc.
The non-verbal communication component should probably also be taken into acccount. Face to face discussions can be more dense of information, since tone and posture can also communicate nuances of beliefs and confidence in them that can make one's position more clear (and often more acceptable). Written communication is very often pretty dry in this respect, resulting sometimes in flame wars and people becoming only more stubborn.
When I was younger, I thought that conversations in real life were much more likely to promote true beliefs and meaningful changes than conversations online, because people in real life were only willing/able to cite evidence they were actually confident in, while those online were able to easily search for arguments favoring their position.
While this is obviously wrong—the concept that people in real life only cite evidence they are justifiably confident in is comically false—I do think the dichotomy illustrated there is interesting. One thing I've noticed is that in general the "rigor" of discussions online is higher (in terms of citations, links to external content, etc.), but that conversations in real life seem still much more likely to actually change people's minds.
I have noticed this effect in both myself and others—what do you think is going on here, and how do you think we might circumvent it? If online discussions could be made more effective at causing people to actually change their minds, this could potentially prove extremely useful.