Great thread - wish this would become a sticky… 
IMO both box modeling and point by point are great methods - as highlighted by the awesome work of Taron and Ripper respectively. I’ve never encountered problems with animating either type of model, just that it obviously pays to keep poly counts down (something I’m still working on!) otherwise fixing facial morphs can become a nightmare.
Also I agree with Larry that looking for facial contours using splines (or alternatively using thin strips of polys) is a great way of getting to know facial topology. To anyone just starting out, I’d say try out all the methods and go with whatever you feel most at ease with - I really don’t think any one process is superior.
One big advantage of point by point I’m not sure anyone’s mentioned is that once you have a generic head model, you can sculpt a variety of faces from the same mesh. Here are two heads I’ve been doodling away at lately - a WIP, both originating from the same basic models…
PS Allenatl, your box modelling screenshots are great - looking forward to giving that a go.










