I echo Mark's opinion that there are too many variables to give you a rule of thumb or standard without knowing more parameters. There are many types of enclosure systems being used by timberframing companies all requiring differing amounts of wood. Conventional stud/fiberglass batt infill is only one of these. The mostly widely embraced enclosure system currently in use is SIP's.
To get even close you would need to define the enclosure system as well as the floor and roof system. Perhaps the only fair way of doing what you are asking is to base it on a single story home built on slab to minimum local structural code and with no architectural features or details.
If you do this and compare a conventional stick built home using lightweight trusses vs. a SIP enclosed timberframe with common rafters I suspect you could possibly see a savings of up to 25-30% in total BF of total lumber used.
Keep in mind that 99% of conventional homes are framed with softwoods. Pine, Fir, Spruce, or Hemlock. Total board ft. in a timberframe can be reduced by using stronger/smaller dimensioned hardwoods such as oak instead of softwood to acheive longer spans and handle greater loads.
Also remeber that from an environmental standpoint a timberframe home can be disassembled and reassembled or the timbers recycled. Conventional framing is for the most part single use.
Hope this helps.
