The train station in my city has 80 million travellers per year compared to the airport which only has 27 million. And while I do not think many train stations have been built since the 1950s many have been expanded.
Definitely not in Germany. There are lots of medium to large cities without an airport, but every one has a large-ish train station with decent connections.
Due to the nature of the two, train stations are usually in the center of cities, while airports have to be quite outside.
Also, in my experience there are usually more than one train station in larger cities but even smaller ones have them. While airports are only a few even at a country level.
I don't know what you mean by "large" then. In the context of this discussion, I meant train stations served by high speed rail and airports with regularly scheduled commercial service. The former vastly outnumbers the latter in continental Europe.