You can either go with facts or emotion. The problem with using too many facts is that people tend to get bored, forgetful, and unsure of how to digest all the data. As Seth Godin writes in his article, Too much data leads to not enough belief, too much data crowds out faith. Rather, too much data overwhelms and causes the listener to stray.
Going with emotion leads to the wrong choices being made because the facts are not really thought out.
If you are the persuader, then using facts or emotion does not matter as long as you get your idea across and people to your side. To the persuaded, emotion counts NOW but facts count later.
I think the best approach is a balance of the two. Carefully chosen facts that can lead to an emotional response: This choice feels right. However, if the person just chooses not to believe the facts, then you have to address the cause of the emotional need to not believe. In some cases, you just cannot win – with that person.
Move on and persuade other people.