I actually have just bought a new EV (VW ID3), and I actually did the Maths. In short, when I charge at home I save about €30 per "tank" compared to my old petrol Car (Skoda Fabia Combi).
If I charge at a public charge station on the EnBW network (which covers most of central and southern Europe), I save about €20 per tank. Please note, I'm based in Germany so your mileage may vary.
We get less distance in the ID3 than in the Skoda (about 300km instead of 400km), but the cost to charge is significantly less, with a full tank costing about €25 at a public charge station compared to the €60 minimum we were paying for the Skoda. So Petrol for a 300km tank would be minimum €45. Hence my calculated €20 saving per 300km. At home the charging cost is between €10-15 per tank, hence the €30 saving.
Please note, these fuel prices were when Petrol in Germany was costing around 180c/L. At the moment, it's closer to 195c/L where I live, so my saving is even more at the moment. When petrol prices come down a bit, or if energy prices go up then, then my saving will reduce, but I dont expect my ID3 will ever be more expensive then my Skoda.
As for charging stations, the EnBW app, lets you see every charging station (on their or associated networks) across Germany and large parts of Europe, tells you how many charging points there are and also whether they are in use. So you can absolutely plan accordingly. However, me and my family dont do massive cross country trips with the car, so our use case may not be representative of everyone, but for us it works massively well.
Anyway, I wanted to put some actual use figures out there. If you've got questions/comments, let me know.