Tankless water heaters are located where the water is being used, so the water can instantly heat up (this reduces water wastage). POU heaters can also end up saving more energy than tankless water heaters that are installed centrally since no hot water is left over in supply pipes after the flow has been shut off.
When it comes to any type of central water heater, whatever cold water is standing in the pipes is dumped down the drain as hot water moves from the heater. This wastage can be avoided, however, but only if a recirculator pump is installed. Although, this will unfortunately be at the cost of the energy to both reheat the water circulated through the pipes, as well as the overall energy to run the pump. Some recirculating systems can reduce standby loss by working only at certain times (ex. turning off late at night). This will end up saving you energy at the expense of a more complex system.