The UK is currently experiencing some prolonged windy weather and my all-renewable energy provider offers dynamic pricing. That means cheap energy and even negative-cost energy. This is where my HA instance shines and saves me a fortune on my power bill. Thanks again to the HA devs for this incredible project.
For the curious, I'm using bottlecapdave's excellent Home Assistant Octopus Energy integration via HACS.
For me the car is the main thing that I can move to cheaper times. I'm also lucky in that I don't need to do that many miles so I can often wait for cheaper times to charge. If I did more miles and needed to charge more frequently/consistently then it would probably be better to have a tariff with a set night rate, sometimes there are decently long stretches where the variable tariff doesn't get as cheap as a night rate would be. On the other side there are days like this where I can get as much into the car as possible and get money back for it.
It definitely depends on your individual usage which would be better. If you're with Octopus, I believe they have a tool which will show you what you would have paid on the variable tariff over the past months, obviously that wouldn't take into account any behavioral changes you would make (or automate) if you had a variable tariff but could still be helpful.
If I had an EV it would make a huge difference. One of the really, really cool features of the Octopus integration is that you can create a binary sensor that triggers for the cheapest hours (consecutive or non-consecutive) between a set time period, so you could create an automation that works out how many hours your car needs to charge at, say, midnight, and have it only charge for the cheapest hours between then and 8am.