Sure they do if it's more pleasant. In the US, the train on the Northeast Corridor takes maybe a bit longer depending upon the specifics than flying and costs in the same ballpark (depending on whether Acela or regular coach, parking, etc.) And it's at capacity at peak times.
When you're not talking big money in the scheme of things, many will take whatever mode of transportation is most convenient and comfortable--especially for business travel.
If you really are very price sensitive, you're probably taking Megabus or something similar.
[0] https://en.wikipedia.org/wiki/High-speed_rail_in_Europe#/med...
A fast train is always a healthier and more pleasant experience than an airplane. Hint: trains have windows.
Disclosure: I'm a private pilot and have lifetime status on two major carriers. I still hate air travel.