In Melbourne, the common method is slab on ground, and I would estimate 80% of new houses use it. If designed properly, it's indestructible, and ideal for filled or problem sites. Only on very steep grades would one consider using timber floor framing and flooring. Timber is more expensive, subject to rot and in termite prone areas, can be attacked by them.
The problems associated with concrete slabs are minor, and with careful design can overcome the biggest problem: shrinkage. Concrete shrinks in it's length by about 1/3-1/2 the distance brickwork grows, so if no expansion/contraction joints are provided to the brick wall, it's not uncommon to see a long brick wall with no joints overhang the concrete slab by up to 1'' to 2''. Structural engineers prefer to pour a house slab in one continuous slab to avoid joints that can heave out of alignment if shear rods are not installed properly. Another problem to watch is to use a flexible adhesive between stone or ceramic tiles, as tiles expand and concrete shrinks.
The older method used where perimeter walls were built first (usually of brick) and the slab poured afterwards insde is no longer used, because of shrinkage and heave problems. The inner ground beneath the slab cannot be comapcted as well as the natural stiff clay under the perimeter wall foundations. Result is differential movement between outer walls and inner walls, showing up as corner cracks in plaster, diagonal cracks over corners of openings and in severe cases, cracked glass due to stressed window frames.
Structural engeneers design slabs to stop differential movement and make allowances for shrinkage and expansion of different materials. It is illegal to construct a residential slab without a structural engineers certificate of compliance and computations in Australia.
Cheers! from Oz.