1-3-4 is often referred to in North America as from the Italian school, and 1-2-4 is often considered French. Although I do not have any studies/numbers to really go on, from what I have gathered 1-2-4 is more common. The benefit of 1-2-4 is the second semitone from 2-4 is stronger, with the consequence of 1-2 not always being wide enough, especially in beginning players who haven't developed the stretch needed or young players with small hands. The opposite arguments could be made of 1-3-4, with 1-3 being stronger and easier to tune, with 3-4 being weaker and often flat.
Joel's system involves the use of both 1-2 and 1-3 for semitones, "four finger technique" where each finger is responsible for a semitone or 1-2-3-4, pivots where the thumb remains stationary and 1-4 can span as far as a major third, and occasionally some other things depending on context. Maintaining a compact hand when possible is also an important part of left hand technique, as a compact hand is stronger, more relaxed, and experiences less fatigue than one maintaining a large stretch.
I would highly recommend Joel's book, but even more so I would recommend trying to find an opportunity to work directly with him or a student of his who has spent a considerable amount of time studying his technique. While the basics can be loosely conveyed via posts here and the text in the book, that "lightbulb" moment of understanding is significantly easier in person.