Anything that requires finer precision than is possible with a finger really. Other use cases include selections (graphics and/or text), hitting a link in the browser without having to zoom first or even the stylus virtual keyboard (for those who have been around long enough to remember it).

I'm firmly on the stylus side. Fingers provide very crude accuracy, make the screen dirty and obscure what you're trying to interact with. On the other hand most of us have opposable thumbs, are trained to use them and prefer using a pen or pencil over finger painting most of the time, even (especially) when writing on a small surface like a tiny notebook, cheque or post-it note.

The only UI area where fingers have an advantage over the stylus is the "pressing a button" use case (like when dialing a phone number), but in those cases actual physical buttons would be much better anyway.