I love to go with the old smokey ones as well as the new high-speed ones.
I really like the interesting experience on night trains and a good breakfast in the morning. And in my opinion it gives you the big advantage of arriving in the centre of a city. Ever gone to Milano for a nice Italian coffee in the morning?
Sometimes there are interesting station buildings, interesting modes of operation, interesting railway paths (e.g. in mountains with all the tunnels and bridges).
It is always very interesting to find out how interesting railway engines work, especially if it is a funicular or rack railway. My first encounter with rack railways was the Schneebergbahn in Austria. It was amazing for me to go up the mountain with a steam-engined train with all the noise and smoke.
Well and then one of the biggest advantages of that way of travelling that you can use your time productively or enjoy the moving landscape, or read a book, chat to other travellers, walk around the aisle if you like to stretch your legs, go to the dining car for a snack or meal. A train is some kind of its own ecosystem.
One might add it is sometimes travelling by train is rather unpredictable: you have to wait for connections, there are delays, sometimes they are crowded with people. Well that may happen. The best thing is to accept it, take it easy and adapt your plans.
Some people state that reading schedules, plan routes is time-consuming. But to me this is one of the most interesting parts in the whole process. An as far as I work for a company which designs scheduling software for railway companies, there is as well a professional interest in how railway systems work.
Well I must confess: I am a train nerd.