Typically the night time rate is much lower, but the price of energy itself is only 1/3rd of the whole bill, the grid company taking another 1/3 and the rest is for taxes, so that smoothes out the price difference.
I'm planning to install solar panels in the near future. The payback time is 7-15 years depending on the amount of DIY work.
You can choose to buy your electricity from anyone but you have to pay the local monopoly for the transfer. Electric transfer/infrastructure has been sold abroad by our very forward thinking smart politicians and thus that money is never seen again.
Both cost double that of electricity or more. So the total is around 13-17c/kWh. Smart metering saves only a few cents per kWh. These two rates have been going up really fast and will lead to a solar/wind revolution in short order.
That's the average energy price, and what typically pay if you have fixed pricing per kWh, but there is lot of variance hourly/seasonally. Sometimes in the night time the price of energy can be almost nothing (e.g. hydro power reverses overfilling), but of course you still have to pay for grid company + taxes. To take advantage of that, you need a "market price" plan with your energy company. E.g. I try to store the cheap night-time energy into water boiler + floor heating.
An electric car is very good match for cheap nigh-time energy, as you typically charge overnight.