After reading some of the comments on the price of train tickets, and while it's true trains are on paper more expensive, there are some things to consider:
* prices and conditions vary between countries. For example, in Germany your children can travel for free until 14, but apparently this is not universal and it can be a big difference for families
* in a lot of countries you can pay for discount cards and get 25/50 percent off. Even in places like Switzerland where the prices are notoriously high, the discount card is comparatively cheap and to my understanding it's valid on pretty much all public transportation (e.g. city trams). If you travel even slightly frequently, it pays for itself quickly.
* similar to planes, trains in some countries offer discounted prices if you book in advance, and for a specific train. E.g. on my last trip to Switzerland, the price was around 160, but I paid 40 for one leg (even first class!) and going back it was 120 because I had the 25% off card. The card itself cost around 60 so it basically was worth it for one trip. When I was a student 10 years ago, I would travel to e.g. Budapest on a German train with their "Europe Special" ticket for 40 (30 with 25% off). You had to book in advance, but this is true for planes as well if you want something really cheap.
* others have commented on this, but there are a ton of external costs for planes and cars. Usually a taxi to the airport, or parking or whatnot. Trains in comparison put you mostly in the city centre and quite often bundle a city ticket so you can hop on a bus, tram or subway to your final destination.
* planes in Europe don't (always?) pay VAT on international travel. that is quite a big difference in the total price
* trains even if not always punctual often come with a guarantee, meaning you can get money back for a delay. In Germany it's 25% if you are more than an hour late, and 50% for two hours. My family spent over two hours a couple days ago sitting on a cramped plane because they could not take off from Berlin, the only thing they can do about it is cry.
There are things that are quite infuriating about trains and train companies, but IMHO their prices are not all that unreasonable. The comfort and speed for short and intermediate trips also has its price im general.