This really depends on the person being persuaded and the type of topic.

For me (and I know many that agree), it's better to put a complex topic into an email than to walk up to people. Organize your thoughts, use bullet points, prioritize the most important things, add web links or other evidence to support your ideas.

The problem is that when you just walk up to my desk or call me on the phone to talk about something complex, you're now forcing me to become your secretary and transcribe your notes. I'm now "writing out your email" that I would prefer you write yourself. That's not being respectful of my time. I can read at ~250 wpm; you can only talk at ~100 wpm.

Yes, if it's something lightweight like you're trying to convince me to go to the Chinese restaurant instead of Italian for lunch, go ahead and talk to me instead of write up an email. Otherwise, please consider if the recipient of your complex topic wants to be your "secretary".

I would be very curious of a survey that asked if people preferred to be convinced by coworkers talking to them instead of writing emails/reports with organized and coherent data. Would it be a minority or majority of respondents?