Prefab can mean all sorts of things. Some modular houses are ‘stick-built’ at a factory, then moved to the site. They may be the same or better quality than a house built on-site, or less. Panelized houses are made from smaller pieces, such as walls manufactured at a factory, then assembled on site. Like modular houses there is a range of quality. Trailer homes can be categorized as pre-fab, and again vary in quality. A ‘stick-built’ house may be built from high quality material, or a lot junk. Prefab trusses are commonly used for roofs in ‘stick-built’ houses, otherwise built on site. Many pre-fab houses are custom built, and you can specify the type of materials used.
IIRC, the Sears homes were built on-site from a set precut materials, making them ‘stick-built’ on site. This method is still used for new houses.
The difference isn’t where the pieces are cut or assembled. It’s the quality of the materials, and the quality of construction. ‘Stick-built’ could refer to a house made primarily of manufactured materials instead of conventional wood boards. Almost all new houses will contain some plywood, a manufactured material.
‘Stick-built’, typically meaning 2x4 type framing is not the ultimate quality in house construction. Log houses, stone houses, and timber frame houses will typically outlast ‘stick-built’ and retain greater value over time. These types of houses are found in the oldest houses still standing.
Most of what would make a house ‘green’ has little to do with it’s construction technique. For stick built and timber-frame houses, the quality of insulation is a major factor. Proper situation to minimize heating and cooling costs are a big factor. The materials chosen are likely to start an argument about what is ‘green’. A log home will require the destruction of a number of whole trees, but doesn’t need to involve the use of plastics which will produce pollution. And the ‘greenest’ house can be in the midst of a large yard, which is maintained with inefficient and highly polluting lawn mowers, weed whackers, and leaf blowers, negating the ‘green’ quality of the house itself.
The main advantage of prefab is lowered costs. Assembly may occur in areas with low cost of living cutting labor costs. If they are built on jigs according to patterns, the time in construction is lowered. The houses, or house parts are usually built indoors, so construction time is not limited by weather considerations. The list of cost advantages is long, but you can generally find prefab houses, or prefabbed components across the range of material quaility, and still save money. Searching the internet tubes should give you plenty of options.