User stories benefit from the fact, that you describe concrete interactions and once you know concrete data and behaviour of the system for it, you might as well add more information about the way you interact. This allows you to use some tools like Cucumber, which with Selenium enables you to translate a story to a test. You might go even further and e.g. for web apps capture all pages you start concrete story at and collect all interactions with that page resulting in some sort of information architecture you might use for documentation or prototyping and later UI testing.
On the other hand, this makes your stories somewhat brittle when it comes to UI changes. I think the agile way of thinking about this is same as when it comes to design changes - do not design for the future, do the simplest possible thing, in the future you might need to change it anyway.
If you stripped your user stories of all concrete things (even inputs) you will end up with use cases(at least in their simplest format, depends on how you write your stories). Use cases are in this respect not brittle at all, they specify only goals. This makes them resistant to change, but its harder to transfer information automatically using tools.
As for the process, RUP/UP derives UI from use cases, but I think agile is in its nature incremental (I will not say iterative, this would exclude agile methods like FDD and Kanban). This means, as you implement new story, you add to your UI what is necessary. This only makes adding UI specifics in stories more reasonable. The problem is, that this is not a very good way to create UI or more generally UX(user experience). This is exactly what one might call a weakpoint of agile. The Agile manifesto concentrates on functional software, but that is it. There are as far as I know no agile techniques for designing UI or UX.