Airtightness and thermal bridging, building breathability, carbon footprint, speed of build, ease of first and second fix etc are all elements that change with the building method.
Blockwork remains the most cost effective building method but when building a low energy house, costs become comparable.
A low energy house can be more easily achieved with timber frame, ICF or SIPS than with a traditional build because a lot of the human error is taken out of the equation – but it all depends on workmanship as block builds will also yield high quality low energy homes (with ample wall cavity widths and good attention to air leakage prevention).
The listed methods above are certainly not exhaustive.
Others include: alternative structural timber options (oak frame or engineered structural timber framing such as glulam), steel frame, stone and modular systems.
These may come at an additional cost, and in many cases you will need to source them from a specialised supplier or another jurisdiction.