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.
Type-ahead works fine with single-threaded GUIs. It was rock solid in Windows 3.1. It worked in nearly all win32 apps because hardly anyone used threads other than for background tasks. But it's broken in most modern UI toolkits and on the web.
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.