Never used a TS-E lens.
Other than for architectural photography (the applications to which I understand), what is the use of this technology?
I see some people using for weddings and portraits - what does this create that a standard WA lens will not?
TS lens can also be used for selective focus, and to radically reduce or increase depth of field. As an example of the latter: Imagine a field of flowers in front of a mountain range. Mere inches in front of the lens is a single flower. A TS lens would allow you to keep everything from the single flower to the mountain range, and the field in between, in sharp focus. Even a wide angle lens with a narrow aperture isn't going to do that. I use this example because it's one I've seen in a book: The book showed one photo taken with a regular wide angle lens, and one with a TS lens. The depth of field for the regular lens was very shallow, despite the wide angle and small aperture.
As an example, on a full-frame DSLR, a 17mm lens at f/22, focused on a flower one foot a way, would give only about six inches DOF. Creative use of a TS lens could result in an infinite DOF.
You've probably also seen examples of the other approach, of giving a very shallow depth of field, when you've seen pictures of a city that appear to be a miniature. A regular wide angle lens, even wide open, would give a very large DOF when focused on buildings hundreds of yards away. TS can reduce that DOF to give the miniature effect.