Many old houses were designed with suspended timber floors. These were designed into houses to keep them dry (at the expense of draughts). The timber joists and floor boards were vented underneath at the front and back of the house to allow a draught to whisk away any rising moisture from the foundations. As long as the vents are open and working and that any intermediate supporting foundation walls retain their air gaps this system can be very effective for keeping moisture out of the wood and hence preventing rot and damp. However these floors can be very draughty and hence energy inefficient as the only material between the house and the outside world is an inch of wood.
In response to draughty floors and some rot in the ends of joists we now commonly replace floors with solid concrete floors. Many of these floors are just solid concrete, most have been fitted with a Damp Proof Membrane (DPM) underneath and some later ones have some insulation installed (the insulation tends to be beneath the slab and also not along the edge). The theory being that the moisture is stopped by the DPM and the wood replaced with a rot-free solution.
So concrete floors are draught-proof, can be insulating and also provide some thermal mass (especially helpful if used in conjunction with underfloor heating / passive solar gain). However, it also drives any rising damp up the adjoining walls. Water will always find a way to escape and if the only option is up an internal wall, so be it. The installation of a solid floor can also block airflow to other rooms. It is common for one room to have its floor replaced. This then can cut off the underfloor ventilation to other rooms. This is turn can cause more problems for the other rooms. So great care is required to ensure that ventilation is maintained where required and that damp is not brought into the house.
Personally I think that wherever possible suspended timber floors should be repaired (the ends can rot) and then the floor be properly insulated and draught proofed. This then gives you a cheaper, less resource intense and future proofed solution that maintains the character of the home as well as not bringing in the potential for damp in the walls.
If insulating the floor then use breathable insulation (as this allows the whole of the floor to breathe) and also a breather membrane (this allows you to create an airtight seal to reduce draughts) and also for any moisture to pass through and dissipate naturally. Care needs to be taken when fitting the membrane as it needs to be taped together to form a consistent barrier and also to be attached to the underfloor walls using a long lasting sealant. Look for products like Orcon F rather than relying in silicon sealers. Conventional stuff just doesn’t last long enough.