You pay a third to a quarter because of differences in electricity tax. And yes, of course Danes piggyback on the Swedish and Norwegian hydro. We supply power in winter from the wind turbines (wind is stronger in winter at Scandinavian latitudes) when water level is low behind the dams, and we buy it in late spring and summer when water is plentiful. It is very much a win/win situation. Nuclear can almost do the same, except it does not have the advantage of automatically supplying more in winter when demand is highest, and it is massively more expensive than wind.
Solar is not of much use in the Scandinavian region so far, since it supplies in summer when the dams are full. Once airconditioning becomes more common, it will start making sense.