In a physical conversation, sources will generally be more open and spontaneous, allowing journalists to build rapport and get good quotes.
But sometimes, an exchange over email will grant your interviewee time to think over the question and their response, where that seems appropriate. Plus, it means you can speak to people which might otherwise prove difficult, such as those in very different time zones or with unpredictable and busy schedules, people with disabilities, and those who simply prefer the text medium.
The problem, according to journalists interviewed (over email) for a Poynter article, is that too often we ask the wrong questions by email. So instead of firing off a quick message to get quotes to plug into your story, try to treat email like any other interview: start with open-ended questions, and have a back-and-forth to ask follow-up questions based on their answers and your other research.
Read the full article for a discussion on the pros and cons of email Q&As and if you do decide to go down that route, how to get them right.