One thing that most TUIs have but most GUIs (web or native app) don't is fast keyboard navigation. There are obviously exceptions to both cases, but as a general rule this seems to hold true.

Watching people who are very familiar with the TUI that they're using do complex business transactions is a sight to behold. In particular, a seasoned user will likely type a series of commands that will get buffered until the TUI catches up with them - I've never seen a GUI that could do this.