There's time to gaze out the window, read, daydream. You can walk to the dining car for lunch, make new friends, indulge in a beer if you feel like it. After all, you're on vacation, and you're not driving. You can look out the window and relax. On top of all my romantic reasons for choosing the train, there are the practical ones.
European trains are fast and reliable.
They're easy and reasonably priced. Eurail and Britrail passes purchased in the United States provide tremendous bargains, and there are no tickets to buy. You just get on the train and go. This gives you freedom and saves precious vacation time. To have the best possible train adventure, pack light.