Post and Beam Walls

Post and Beam/Timber Frame - A post and beam structure differs from a standard "stick frame" structure in that rather than using smaller size lumber like 2x4s or 2x6s spaced 16 or 24 inches apart, it uses more sizable lumber like 4x4s and 6x6s or larger spaced 4 feet or more apart.  Structurally, timber framing is a post and beam method, and although traditional timber framing didn't use nails, there is not a significant difference between  the two. The biggest difference in in  implication: in timber framing the large dimensional pieces of lumber are usually left exposed, while a in a post and beam they may or may not be exposed.

Timber frame or post and beam structures are very commonly used in strawbale, light clay and papercrete buildings: the insulating material in this case is called infill since it does not carry any load.  In places where there is lateral loading (wind, earthquake), some kind of skin will be required to pick up that load.  Timber framing is also combined with SIPs, although this is obviously overkill since building with SIPs generally requires few structural members.  It could also be combined with non-load bearing standard construction, but there is no real benefit to doing so unless you're trying to use all non structural studs.  In fact in many timber frame buildings, the main reason for the timber frame is aesthetics, not saving materials or using alternative building techniques.

For alternative infill buildings, an alternative to post and beam structure is to use site-built box beams.   These are constructed from 2x material and plywood, and are significantly stronger than the component materials.

There are various claims out there that timber framing/post and beam uses less wood than stick framing, but it does not appear that this happens very often in practice.  When the wall in-fill is straw, cob or equivalent, at least the plywood wall sheathing is eliminated--a significant savings in wood.  The counterpoint to this is that ceilings and roofs are still the same, and the alterative methods often need additional wood for attaching things: around windows and doors, wood to hang cabinets from, blocking to hang things like towel bars etc.

Although there has been a move away from larger beams (or at least toward engineered wood) in order to reduce pressure to cut old growth forests, this conventional wisdom may be less relevant when applied to FSC certified beams.  By buying larger beams, you're encouraging the woodlot owners to cut some trees on a longer rotation, promoting a forest that is more ecological robust.

Summary:  there is a significant learning curve, but nothing any experienced carpenter would have a hard time with.  Since timber frame is usually combined with some other method, it is hard to comment on the benefits of it alone.  Timber frame is often chosen for the look.