It depends where you are located and which method is more commonly used, which would dictate labor cost for construction.

Wood is a more forgiving method, meaning changes in design are easier to make compared to concrete. Material is also cheaper and there is no 'curing' time.

What are you building? A house or a fence?

Concrete has its advantages. They are quite sound proof and extremely solidly built. It is on the down side more expensive and harder to renovate down the road. If you know what you want and dont plan on changing your mind during construction. Then concrete is the better option, it is a fortress compared to stick built

As a veteran builder who has built concrete homes as far north as northern Minnesota to the southern coast of Georgia if money were no option concrete would always be my first choice. Depending on your region and climate different rules apply but the principle is the same. Up north we used foam insulated forms that us a fiberglass interior "stud" to which drywall can be applied to interior walls look and feels like traditional construction. You need to find electrical contractors use to working in this special environment . Our heating systems were in floor radiant heat. In the south we used the same heating system and added forced air cooling through the ceiling systems. Heat and cooling costs minimized due to super insulation. We have build single and multiple stories with solid concrete. Use a good architect familiar with residential concrete. We build solid poured systems as opposed to cored block.
Cost aside ...concrete all the way. Good luck.

Thanks for all of the feedback. I am in Mobile Alabama and planning on building around 2,500 sq ft 2 story house.