Good morning Shazia,
It should not be confusion between relative weight of activities to each other (based on cost or M/H) and progress measurement.
Explaining:
Method of measurement for construction should stick allways to physical progress of the works such as Units, m3, klms, tons, etc, done. Then comparing with the total qty to be done it comes a % achieved.
Since normaly you have activities with diferent units of physical work (m3, tons, m2, etc) then you have to use the same unit to relative calculate all the progress of the works - therefore MH is the comun unit to give a relative weight to each activity.
Summarizing:
M/H - Use as units for work qty and as relative weight of each activity.
Qtys (m3, m2, tons, inches) - Use for physical progress of works.
Choosing between M/H and cost: Depends on the kind of projects, activities, etc. Basically boths are suitable.
Hope it helps you.
BR
JMFrade