Well, in person, you can place a face with a name. Establish a personal relationship, ect.
Over the phone- seems slowest and most cumbersome to me, just my opinion.
Online- a good hybrid of both. It is faster in my opinion because I can get right to work on the preapproval. Maybe call and ask a couple questions on incomplete answers at the most.
Then, I usually call or set up an appointment to discuss options, collect documentation, ect.
A face to face is really not quicker but it really is a personal preference.
You are in the drivers seat, do it the way you see fit.