Is it better to negotiate a faculty offer by email or phone?
Negotiating the conditions of any future employment is an important conversation.

Most of human communication is non-verbal. We communicate a lot through our voice tone and body language. 

Some people avoid face-to-face, or telephone conversations, as they find the interaction awkward. Ask yourself:- if you were the search committee chair, would you want to employ someone as a lecturer who was uncomfortable in face-to-face communication?

At least offer to have a telephone conversation, or Skype, or video conference with the other party, if a face-to-face meeting is impractical or inappropriate. This shows you are keen to engage in the most efficient means of human-to-human communication. Then follow this up with an email clarifying the main points of your conversation.