Ahuh. OK, well sundry distractions later, I was just chilling outside with a glass of wine and me whippet and the missus in the cool of the evening, when the cynical side of me decided to fish the mobile out and create a form with a multi-line text box on it. Guess what? Tabs work perfectly!
There is no simple facility for changing the size used by a tab, but then there isn't in the big boys world either, so you have to do something clever to vary the tab size.
I'm really not sure what we are supposed to see as other wrappings in big Windows differ. The Delphi TMemo (the closest they get to a multi-line TextBox) has extra bits that for example VBA in Excel doesn't. The VBA version doesn't do Tabs, the Delphi one does, but just as here Delphi gives no immediate control of tab size. The Delphi TRichEdit doesn't give any tab size control either. But both Delphi wrappers provide a WantTabs property which can conveniently switch support on and off. (It's years since I used these in Delphi, so I may have missed something).
So, the TextBox in the library has tab support added (as it doesn't seem to be native), but then the box in the dev ide has either taken it away again, or is a more basic version. You'd need to look closely at the source code to figure what is the actual case. Perhaps our glorious leader could just tell us?
Whatever, my guess is that it is the tab size issue which stopped the TextBox (as per the library) being used in the dev ide.
Umm, TRichEdit, as Delphi calls it. There must be something similar for CF because Word Mobile exists. But may be WM is like your html thingummy and not the real McCoy. Baffled of Fleet.