Generally speaking, a single-storey ground-floor extension tends to be less expensive than adding a second storey to an existing home. Building up requires significant structural work, as the existing walls and footings need to be assessed and potentially upgraded to carry the additional load.
You also need to factor in the cost of a temporary staircase, temporary accommodation if the home becomes unliveable during construction, and the complexity of working around an occupied space.
That said, building up can be the better option on smaller blocks where land area is limited, and in some cases the cost per square metre can be comparable once all factors are considered. The right answer depends on your block, your home, and your goals.
Mitroteam Projects can assess both options and give you honest advice on what makes sense for your situation.